Sobolev Spaces Of Fractional Order Nemytskij Operators And Nonlinear Partial Differential Equations

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Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations

Author : Thomas Runst
Publisher : Walter de Gruyter
ISBN 13 : 9783110151138
Total Pages : 568 pages
Book Rating : 4.1/5 (511 download)

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Book Synopsis Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations by : Thomas Runst

Download or read book Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations written by Thomas Runst and published by Walter de Gruyter. This book was released on 1996 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief Jürgen Appell, Würzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Louis Nirenberg, New York, USA Alfonso Vignoli, Rome, Italy Editorial Board Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Toruń, Poland Vicenţiu D. Rădulescu, Kraków, Poland Simeon Reich, Haifa, Israel Please submit book proposals to Jürgen Appell. Titles in planning include Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Tomasz W. Dłotko and Yejuan Wang, Critical Parabolic-Type Problems (2019) Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019) Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations

Author : Thomas Runst
Publisher : Walter de Gruyter
ISBN 13 : 311081241X
Total Pages : 561 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations by : Thomas Runst

Function Spaces, Differential Operators and Nonlinear Analysis

Author : Dorothee Haroske
Publisher : Birkhäuser
ISBN 13 : 3034880359
Total Pages : 462 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Function Spaces, Differential Operators and Nonlinear Analysis by : Dorothee Haroske

Download or read book Function Spaces, Differential Operators and Nonlinear Analysis written by Dorothee Haroske and published by Birkhäuser. This book was released on 2012-12-06 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to our teacher and friend Hans Triebel. The core of the book is based on lectures given at the International Conference "Function Spaces, Differential Operators and Nonlinear Analysis" (FSDONA--01) held in Teistungen, Thuringia / Germany, from June 28 to July 4,2001, in honour of his 65th birthday. This was the fifth in a series of meetings organised under the same name by scientists from Finland (Helsinki, Oulu) , the Czech Republic (Prague, Plzen) and Germany (Jena) promoting the collaboration of specialists in East and West, working in these fields. This conference was a very special event because it celebrated Hans Triebel's extraordinary impact on mathematical analysis. The development of the mod ern theory of function spaces in the last 30 years and its application to various branches in both pure and applied mathematics is deeply influenced by his lasting contributions. In a series of books Hans Triebel has given systematic treatments of the theory of function spaces from different points of view, thus revealing its interdependence with interpolation theory, harmonic analysis, partial differential equations, nonlinear operators, entropy, spectral theory and, most recently, anal ysis on fractals. The presented collection of papers is a tribute to Hans Triebel's distinguished work. The book is subdivided into three parts: • Part I contains the two invited lectures by O.V. Besov (Moscow) and D.E. Edmunds (Sussex) having a survey character and honouring Hans Triebel's contributions.

A Short Introduction to Partial Differential Equations

Author : Arian Novruzi
Publisher : Springer Nature
ISBN 13 : 3031395247
Total Pages : 225 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis A Short Introduction to Partial Differential Equations by : Arian Novruzi

Download or read book A Short Introduction to Partial Differential Equations written by Arian Novruzi and published by Springer Nature. This book was released on 2023-12-30 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a short introduction to partial differential equations (PDEs). It is primarily addressed to graduate students and researchers, who are new to PDEs. The book offers a user-friendly approach to the analysis of PDEs, by combining elementary techniques and fundamental modern methods. The author focuses the analysis on four prototypes of PDEs, and presents two approaches for each of them. The first approach consists of the method of analytical and classical solutions, and the second approach consists of the method of weak (variational) solutions. In connection with the approach of weak solutions, the book also provides an introduction to distributions, Fourier transform and Sobolev spaces. The book ends with an appendix chapter, which complements the previous chapters with proofs, examples and remarks. This book can be used for an intense one-semester, or normal two-semester, PDE course. The reader is expected to have knowledge of linear algebra and of differential equations, a good background in real and complex calculus and a modest background in analysis and topology. The book has many examples, which help to better understand the concepts, highlight the key ideas and emphasize the sharpness of results, as well as a section of problems at the end of each chapter.

Function Spaces and Partial Differential Equations

Author : Ali Taheri
Publisher : Oxford Lecture Mathematics and
ISBN 13 : 0198733151
Total Pages : 481 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Function Spaces and Partial Differential Equations by : Ali Taheri

Download or read book Function Spaces and Partial Differential Equations written by Ali Taheri and published by Oxford Lecture Mathematics and. This book was released on 2015 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains

Author : Mikhail S. Agranovich
Publisher : Springer
ISBN 13 : 3319146483
Total Pages : 331 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains by : Mikhail S. Agranovich

Download or read book Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains written by Mikhail S. Agranovich and published by Springer. This book was released on 2015-05-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems. The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory and pseudodifferential operators, has included his own very recent findings in the present book. The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date. Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory and mathematical physics will find this book particularly valuable.

Methods for Partial Differential Equations

Author : Marcelo R. Ebert
Publisher : Birkhäuser
ISBN 13 : 3319664565
Total Pages : 456 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Methods for Partial Differential Equations by : Marcelo R. Ebert

Download or read book Methods for Partial Differential Equations written by Marcelo R. Ebert and published by Birkhäuser. This book was released on 2018-02-23 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory. It also discusses the notion of energy of solutions, a highly effective tool for the treatment of non-stationary or evolution models and shows how to define energies for different models. Part 3 demonstrates how phase space analysis and interpolation techniques are used to prove decay estimates for solutions on and away from the conjugate line. It also examines how terms of lower order (mass or dissipation) or additional regularity of the data may influence expected results. Part 4 addresses semilinear models with power type non-linearity of source and absorbing type in order to determine critical exponents: two well-known critical exponents, the Fujita exponent and the Strauss exponent come into play. Depending on concrete models these critical exponents divide the range of admissible powers in classes which make it possible to prove quite different qualitative properties of solutions, for example, the stability of the zero solution or blow-up behavior of local (in time) solutions. The last part features selected research projects and general background material.

Beyond Sobolev and Besov

Author : Cornelia Schneider
Publisher : Springer Nature
ISBN 13 : 3030751392
Total Pages : 339 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Beyond Sobolev and Besov by : Cornelia Schneider

Download or read book Beyond Sobolev and Besov written by Cornelia Schneider and published by Springer Nature. This book was released on 2021-05-31 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the close relation between quite sophisticated function spaces, the regularity of solutions of partial differential equations (PDEs) in these spaces and the link with the numerical solution of such PDEs. It consists of three parts. Part I, the introduction, provides a quick guide to function spaces and the general concepts needed. Part II is the heart of the monograph and deals with the regularity of solutions in Besov and fractional Sobolev spaces. In particular, it studies regularity estimates of PDEs of elliptic, parabolic and hyperbolic type on non smooth domains. Linear as well as nonlinear equations are considered and special attention is paid to PDEs of parabolic type. For the classes of PDEs investigated a justification is given for the use of adaptive numerical schemes. Finally, the last part has a slightly different focus and is concerned with traces in several function spaces such as Besov– and Triebel–Lizorkin spaces, but also in quite general smoothness Morrey spaces. The book is aimed at researchers and graduate students working in regularity theory of PDEs and function spaces, who are looking for a comprehensive treatment of the above listed topics.

Perspectives in Partial Differential Equations, Harmonic Analysis and Applications

Author : Dorina Mitrea
Publisher : American Mathematical Soc.
ISBN 13 : 0821844245
Total Pages : 446 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Perspectives in Partial Differential Equations, Harmonic Analysis and Applications by : Dorina Mitrea

Download or read book Perspectives in Partial Differential Equations, Harmonic Analysis and Applications written by Dorina Mitrea and published by American Mathematical Soc.. This book was released on 2008 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers contributed on the occasion of Mazya's 70th birthday by a distinguished group of experts of international stature in the fields of harmonic analysis, partial differential equations, function theory, and spectral analysis, reflecting the state of the art in these areas.

Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces

Author : Ariel Barton:
Publisher : American Mathematical Soc.
ISBN 13 : 1470419890
Total Pages : 110 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces by : Ariel Barton:

Download or read book Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces written by Ariel Barton: and published by American Mathematical Soc.. This book was released on 2016-09-06 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted Lp classes. The authors establish: (1) Mapping properties for the double and single layer potentials, as well as the Newton potential; (2) Extrapolation-type solvability results: the fact that solvability of the Dirichlet or Neumann boundary value problem at any given Lp space automatically assures their solvability in an extended range of Besov spaces; (3) Well-posedness for the non-homogeneous boundary value problems. In particular, the authors prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric, coefficients.

New Tools for Nonlinear PDEs and Application

Author : Marcello D'Abbicco
Publisher : Springer
ISBN 13 : 3030109372
Total Pages : 390 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis New Tools for Nonlinear PDEs and Application by : Marcello D'Abbicco

Download or read book New Tools for Nonlinear PDEs and Application written by Marcello D'Abbicco and published by Springer. This book was released on 2019-05-07 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features a collection of papers devoted to recent results in nonlinear partial differential equations and applications. It presents an excellent source of information on the state-of-the-art, new methods, and trends in this topic and related areas. Most of the contributors presented their work during the sessions "Recent progress in evolution equations" and "Nonlinear PDEs" at the 12th ISAAC congress held in 2017 in Växjö, Sweden. Even if inspired by this event, this book is not merely a collection of proceedings, but a stand-alone project gathering original contributions from active researchers on the latest trends in nonlinear evolution PDEs.

Modulation Spaces

Author : Árpád Bényi
Publisher : Springer Nature
ISBN 13 : 1071603329
Total Pages : 177 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Modulation Spaces by : Árpád Bényi

Download or read book Modulation Spaces written by Árpád Bényi and published by Springer Nature. This book was released on 2020-02-22 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph serves as a much-needed, self-contained reference on the topic of modulation spaces. By gathering together state-of-the-art developments and previously unexplored applications, readers will be motivated to make effective use of this topic in future research. Because modulation spaces have historically only received a cursory treatment, this book will fill a gap in time-frequency analysis literature, and offer readers a convenient and timely resource. Foundational concepts and definitions in functional, harmonic, and real analysis are reviewed in the first chapter, which is then followed by introducing modulation spaces. The focus then expands to the many valuable applications of modulation spaces, such as linear and multilinear pseudodifferential operators, and dispersive partial differential equations. Because it is almost entirely self-contained, these insights will be accessible to a wide audience of interested readers. Modulation Spaces will be an ideal reference for researchers in time-frequency analysis and nonlinear partial differential equations. It will also appeal to graduate students and seasoned researchers who seek an introduction to the time-frequency analysis of nonlinear dispersive partial differential equations.

Besov Regularity of Stochastic Partial Differential Equations on Bounded Lipschitz Domains

Author : Petru A. Cioica
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832539204
Total Pages : 162 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis Besov Regularity of Stochastic Partial Differential Equations on Bounded Lipschitz Domains by : Petru A. Cioica

Download or read book Besov Regularity of Stochastic Partial Differential Equations on Bounded Lipschitz Domains written by Petru A. Cioica and published by Logos Verlag Berlin GmbH. This book was released on 2015-03-01 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic partial differential equations (SPDEs, for short) are the mathematical models of choice for space time evolutions corrupted by noise. Although in many settings it is known that the resulting SPDEs have a unique solution, in general, this solution is not given explicitly. Thus, in order to make those mathematical models ready to use for real life applications, appropriate numerical algorithms are needed. To increase efficiency, it would be tempting to design suitable adaptive schemes based, e.g., on wavelets. However, it is not a priori clear whether such adaptive strategies can outperform well-established uniform alternatives. Their theoretical justification requires a rigorous regularity analysis in so-called non-linear approximation scales of Besov spaces. In this thesis the regularity of (semi-)linear second order SPDEs of Itô type on general bounded Lipschitz domains is analysed. The non-linear approximation scales of Besov spaces are used to measure the regularity with respect to the space variable, the time regularity being measured first in terms of integrability and afterwards in terms of Hölder norms. In particular, it is shown that in specific situations the spatial Besov regularity of the solution in the non-linear approximation scales is generically higher than its corresponding classical Sobolev regularity. This indicates that it is worth developing spatially adaptive wavelet methods for solving SPDEs instead of using uniform alternatives.

Hamiltonian Partial Differential Equations and Applications

Author : Philippe Guyenne
Publisher : Springer
ISBN 13 : 149392950X
Total Pages : 449 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Hamiltonian Partial Differential Equations and Applications by : Philippe Guyenne

Download or read book Hamiltonian Partial Differential Equations and Applications written by Philippe Guyenne and published by Springer. This book was released on 2015-09-11 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.

Stochastic Differential Equations

Author : Peter H. Baxendale
Publisher : World Scientific
ISBN 13 : 9812770631
Total Pages : 416 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Stochastic Differential Equations by : Peter H. Baxendale

Download or read book Stochastic Differential Equations written by Peter H. Baxendale and published by World Scientific. This book was released on 2007 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of 15 articles written by experts in stochastic analysis. The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract the attention of mathematicians of all generations. Together with a short but thorough introduction to SPDEs, it presents a number of optimal, and essentially unimprovable, results about solvability for a large class of both linear and non-linear equations. The other papers in this volume were specially written for the occasion of Prof RozovskiiOCOs 60th birthday. They tackle a wide range of topics in the theory and applications of stochastic differential equations, both ordinary and with partial derivatives."

Multi-Valued Variational Inequalities and Inclusions

Author : Siegfried Carl
Publisher : Springer Nature
ISBN 13 : 3030651657
Total Pages : 596 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Multi-Valued Variational Inequalities and Inclusions by : Siegfried Carl

Download or read book Multi-Valued Variational Inequalities and Inclusions written by Siegfried Carl and published by Springer Nature. This book was released on 2021-03-02 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a large class of multi-valued variational differential inequalities and inclusions of stationary and evolutionary types with constraints reflected by subdifferentials of convex functionals. Its main goal is to provide a systematic, unified, and relatively self-contained exposition of existence, comparison and enclosure principles, together with other qualitative properties of multi-valued variational inequalities and inclusions. The problems under consideration are studied in different function spaces such as Sobolev spaces, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents, and Beppo-Levi spaces. A general and comprehensive sub-supersolution method (lattice method) is developed for both stationary and evolutionary multi-valued variational inequalities, which preserves the characteristic features of the commonly known sub-supersolution method for single-valued, quasilinear elliptic and parabolic problems. This method provides a powerful tool for studying existence and enclosure properties of solutions when the coercivity of the problems under consideration fails. It can also be used to investigate qualitative properties such as the multiplicity and location of solutions or the existence of extremal solutions. This is the first in-depth treatise on the sub-supersolution (lattice) method for multi-valued variational inequalities without any variational structures, together with related topics. The choice of the included materials and their organization in the book also makes it useful and accessible to a large audience consisting of graduate students and researchers in various areas of Mathematical Analysis and Theoretical Physics.

New Prospects in Direct, Inverse and Control Problems for Evolution Equations

Author : Angelo Favini
Publisher : Springer
ISBN 13 : 3319114069
Total Pages : 472 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis New Prospects in Direct, Inverse and Control Problems for Evolution Equations by : Angelo Favini

Download or read book New Prospects in Direct, Inverse and Control Problems for Evolution Equations written by Angelo Favini and published by Springer. This book was released on 2014-11-27 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences. Applied sciences consider situations in which the evolution of a given system over time is observed, and the related models can be formulated in terms of evolution equations (EEs). These equations have been studied intensively in theoretical research and are the source of an enormous number of applications. In this volume, particular attention is given to direct, inverse and control problems for EEs. The book provides an updated overview of the field, revealing its richness and vitality.