Sobolev Spaces Their Generalizations And Elliptic Problems In Smooth And Lipschitz Domains

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

Author : Mikhail S. Agranovich
Publisher : Springer
ISBN 13 : 3319146483
Total Pages : 343 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 343 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.

Distributions, Sobolev Spaces, Elliptic Equations

Author : Dorothee Haroske
Publisher : European Mathematical Society
ISBN 13 : 9783037190425
Total Pages : 312 pages
Book Rating : 4.1/5 (94 download)

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Book Synopsis Distributions, Sobolev Spaces, Elliptic Equations by : Dorothee Haroske

Download or read book Distributions, Sobolev Spaces, Elliptic Equations written by Dorothee Haroske and published by European Mathematical Society. This book was released on 2007 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is the main aim of this book to develop at an accessible, moderate level an $L_2$ theory for elliptic differential operators of second order on bounded smooth domains in Euclidean n-space, including a priori estimates for boundary-value problems in terms of (fractional) Sobolev spaces on domains and on their boundaries, together with a related spectral theory. The presentation is preceded by an introduction to the classical theory for the Laplace-Poisson equation, and some chapters provide required ingredients such as the theory of distributions, Sobolev spaces and the spectral theory in Hilbert spaces. The book grew out of two-semester courses the authors have given several times over a period of ten years at the Friedrich Schiller University of Jena. It is addressed to graduate students and mathematicians who have a working knowledge of calculus, measure theory and the basic elements of functional analysis (as usually covered by undergraduate courses) and who are seeking an accessible introduction to some aspects of the theory of function spaces and its applications to elliptic equations.

Analysis as a Life

Author : Sergei Rogosin
Publisher : Springer
ISBN 13 : 3030026507
Total Pages : 318 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Analysis as a Life by : Sergei Rogosin

Download or read book Analysis as a Life written by Sergei Rogosin and published by Springer. This book was released on 2019-01-30 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book comprising selected papers of colleagues and friends of Heinrich Begehr on the occasion of his 80th birthday. It aims at being a tribute to the excellent achievements of Heinrich Begehr in complex analysis and complex differential equations, and especially to his prominent role as one of the creators and long-time leader of the International Society for Analysis, its Applications and Computation (ISAAC).

Variational Techniques for Elliptic Partial Differential Equations

Author : Francisco J. Sayas
Publisher : CRC Press
ISBN 13 : 0429016204
Total Pages : 492 pages
Book Rating : 4.4/5 (29 download)

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Book Synopsis Variational Techniques for Elliptic Partial Differential Equations by : Francisco J. Sayas

Download or read book Variational Techniques for Elliptic Partial Differential Equations written by Francisco J. Sayas and published by CRC Press. This book was released on 2019-01-16 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variational Techniques for Elliptic Partial Differential Equations, intended for graduate students studying applied math, analysis, and/or numerical analysis, provides the necessary tools to understand the structure and solvability of elliptic partial differential equations. Beginning with the necessary definitions and theorems from distribution theory, the book gradually builds the functional analytic framework for studying elliptic PDE using variational formulations. Rather than introducing all of the prerequisites in the first chapters, it is the introduction of new problems which motivates the development of the associated analytical tools. In this way the student who is encountering this material for the first time will be aware of exactly what theory is needed, and for which problems. Features A detailed and rigorous development of the theory of Sobolev spaces on Lipschitz domains, including the trace operator and the normal component of vector fields An integration of functional analysis concepts involving Hilbert spaces and the problems which can be solved with these concepts, rather than separating the two Introduction to the analytical tools needed for physical problems of interest like time-harmonic waves, Stokes and Darcy flow, surface differential equations, Maxwell cavity problems, etc. A variety of problems which serve to reinforce and expand upon the material in each chapter, including applications in fluid and solid mechanics

From Complex Analysis to Operator Theory: A Panorama

Author : Malcolm Brown
Publisher : Springer Nature
ISBN 13 : 3031311396
Total Pages : 731 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis From Complex Analysis to Operator Theory: A Panorama by : Malcolm Brown

Download or read book From Complex Analysis to Operator Theory: A Panorama written by Malcolm Brown and published by Springer Nature. This book was released on 2023-09-21 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Naboko’s scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.

Integral Methods in Science and Engineering

Author : Christian Constanda
Publisher : Springer Nature
ISBN 13 : 303134099X
Total Pages : 407 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Integral Methods in Science and Engineering by : Christian Constanda

Download or read book Integral Methods in Science and Engineering written by Christian Constanda and published by Springer Nature. This book was released on 2023-10-31 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of articles on state-of-the-art developments in the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Seventeenth International Conference on Integral Methods in Science and Engineering, held virtually in July 2022, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical, electrical, and petroleum engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential working tool.

Boundary Value Problems, Weyl Functions, and Differential Operators

Author : Jussi Behrndt
Publisher : Springer Nature
ISBN 13 : 3030367142
Total Pages : 772 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Boundary Value Problems, Weyl Functions, and Differential Operators by : Jussi Behrndt

Download or read book Boundary Value Problems, Weyl Functions, and Differential Operators written by Jussi Behrndt and published by Springer Nature. This book was released on 2020-01-03 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.

An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space

Author : Konrad Schmüdgen
Publisher : Springer Nature
ISBN 13 : 3030463664
Total Pages : 381 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space by : Konrad Schmüdgen

Download or read book An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space written by Konrad Schmüdgen and published by Springer Nature. This book was released on 2020-07-28 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.

Mathematical Modeling and Supercomputer Technologies

Author : Dmitry Balandin
Publisher : Springer Nature
ISBN 13 : 3030787591
Total Pages : 418 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Mathematical Modeling and Supercomputer Technologies by : Dmitry Balandin

Download or read book Mathematical Modeling and Supercomputer Technologies written by Dmitry Balandin and published by Springer Nature. This book was released on 2021-06-23 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes selected and revised papers from the 20th International Conference on Mathematical Modeling and Supercomputer Technologies, MMST 2020, held in Nizhny Novgorod, Russia, in November 2020. Due to the COVID-19 pandemic the conference was held online. The 25 full papers and 8 short papers presented in the volume were thoroughly reviewed and selected from the 106 submissions. They are organized in topical secions on computational methods for mathematical models analysis; computation in optimization and optimal control; supercomputer simulation.

Boundary Stabilization of Parabolic Equations

Author : Ionuţ Munteanu
Publisher : Springer
ISBN 13 : 3030110990
Total Pages : 214 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Boundary Stabilization of Parabolic Equations by : Ionuţ Munteanu

Download or read book Boundary Stabilization of Parabolic Equations written by Ionuţ Munteanu and published by Springer. This book was released on 2019-02-15 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The potential control applications of this technique are wide ranging in many research areas, such as Newtonian fluid flows modeled by the Navier-Stokes equations; electrically conducted fluid flows; phase separation modeled by the Cahn-Hilliard equations; and deterministic or stochastic semi-linear heat equations arising in biology, chemistry, and population dynamics modeling. The text provides answers to the following problems, which are of great practical importance: Designing the feedback law using a minimal set of eigenfunctions of the linear operator obtained from the linearized equation around the target state Designing observers for the considered control systems Constructing time-discrete controllers requiring only partial knowledge of the state After reviewing standard notations and results in functional analysis, linear algebra, probability theory and PDEs, the author describes his novel stabilization algorithm. He then demonstrates how this abstract model can be applied to stabilization problems involving magnetohydrodynamic equations, stochastic PDEs, nonsteady-states, and more. Boundary Stabilization of Parabolic Equations will be of particular interest to researchers in control theory and engineers whose work involves systems control. Familiarity with linear algebra, operator theory, functional analysis, partial differential equations, and stochastic partial differential equations is required.

The Application of Mathematics to Physics and Nonlinear Science

Author : Andrei Ludu
Publisher : MDPI
ISBN 13 : 3039287265
Total Pages : 122 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis The Application of Mathematics to Physics and Nonlinear Science by : Andrei Ludu

Download or read book The Application of Mathematics to Physics and Nonlinear Science written by Andrei Ludu and published by MDPI. This book was released on 2020-04-16 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear science is the science of, among other exotic phenomena, unexpected and unpredictable behavior, catastrophes, complex interactions, and significant perturbations. Ocean and atmosphere dynamics, weather, many bodies in interaction, ultra-high intensity excitations, life, formation of natural patterns, and coupled interactions between components or different scales are only a few examples of systems where nonlinear science is necessary. All outstanding, self-sustained, and stable structures in space and time exist and protrude out of a regular linear background of states mainly because they identify themselves from the rest by being highly localized in range, time, configuration, states, and phase spaces. Guessing how high up you drive toward the top of the mountain by compiling your speed, road slope, and trip duration is a linear model, but predicting the occurrence around a turn of a boulder fallen on the road is a nonlinear phenomenon. In an effort to grasp and understand nonlinear phenomena, scientists have developed several mathematical approaches including inverse scattering theory, Backlund and groups of transformations, bilinear method, and several other detailed technical procedures. In this Special Issue, we introduce a few very recent approaches together with their physical meaning and applications. We present here five important papers on waves, unsteady flows, phases separation, ocean dynamics, nonlinear optic, viral dynamics, and the self-appearance of patterns for spatially extended systems, which are problems that have aroused scientists’ interest for decades, yet still cannot be predicted and have their generating mechanism and stability open to debate. The aim of this Special Issue was to present these most debated and interesting topics from nonlinear science for which, despite the existence of highly developed mathematical tools of investigation, there are still fundamental open questions.

Sobolev Spaces

Author : Vladimir Maz'ya
Publisher : Springer
ISBN 13 : 3662099225
Total Pages : 506 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Sobolev Spaces by : Vladimir Maz'ya

Download or read book Sobolev Spaces written by Vladimir Maz'ya and published by Springer. This book was released on 2013-12-21 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Sobolev spaces, i. e. the classes of functions with derivatives in L , occupy p an outstanding place in analysis. During the last two decades a substantial contribution to the study of these spaces has been made; so now solutions to many important problems connected with them are known. In the present monograph we consider various aspects of Sobolev space theory. Attention is paid mainly to the so called imbedding theorems. Such theorems, originally established by S. L. Sobolev in the 1930s, proved to be a useful tool in functional analysis and in the theory of linear and nonlinear par tial differential equations. We list some questions considered in this book. 1. What are the requirements on the measure f1, for the inequality q

Sobolev Spaces on Domains

Author : Victor I. Burenkov
Publisher : Springer-Verlag
ISBN 13 : 3663113744
Total Pages : 312 pages
Book Rating : 4.6/5 (631 download)

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Book Synopsis Sobolev Spaces on Domains by : Victor I. Burenkov

Download or read book Sobolev Spaces on Domains written by Victor I. Burenkov and published by Springer-Verlag. This book was released on 2013-07-02 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Sobolev Spaces

Author : Erhan Pişkin
Publisher : Bentham Science Publishers
ISBN 13 : 1681089149
Total Pages : 203 pages
Book Rating : 4.6/5 (81 download)

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Book Synopsis An Introduction to Sobolev Spaces by : Erhan Pişkin

Download or read book An Introduction to Sobolev Spaces written by Erhan Pişkin and published by Bentham Science Publishers. This book was released on 2021-11-10 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sobolev spaces were firstly defined by the Russian mathematician, Sergei L. Sobolev (1908-1989) in the 1930s. Several properties of these spaces have been studied by mathematicians until today. Functions that account for existence and uniqueness, asymptotic behavior, blow up, stability and instability of the solution of many differential equations that occur in applied and in engineering sciences are carried out with the help of Sobolev spaces and embedding theorems in these spaces. An Introduction to Sobolev Spaces provides a brief introduction to Sobolev spaces at a simple level with illustrated examples. Readers will learn about the properties of these types of vector spaces and gain an understanding of advanced differential calculus and partial difference equations that are related to this topic. The contents of the book are suitable for undergraduate and graduate students, mathematicians, and engineers who have an interest in getting a quick, but carefully presented, mathematically sound, basic knowledge about Sobolev Spaces.

A First Course in Fractional Sobolev Spaces

Author : Giovanni Leoni
Publisher : American Mathematical Society
ISBN 13 : 1470472538
Total Pages : 605 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A First Course in Fractional Sobolev Spaces by : Giovanni Leoni

Download or read book A First Course in Fractional Sobolev Spaces written by Giovanni Leoni and published by American Mathematical Society. This book was released on 2023-03-17 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a gentle introduction to fractional Sobolev spaces which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of one variable. It covers the definition, standard properties, extensions, embeddings, Hardy inequalities, and interpolation inequalities. The second part deals with fractional Sobolev spaces of several variables. The author studies completeness, density, homogeneous fractional Sobolev spaces, embeddings, necessary and sufficient conditions for extensions, Gagliardo-Nirenberg type interpolation inequalities, and trace theory. The third part explores some applications: interior regularity for the Poisson problem with the right-hand side in a fractional Sobolev space and some basic properties of the fractional Laplacian. The first part of the book is accessible to advanced undergraduates with a strong background in integration theory; the second part, to graduate students having familiarity with measure and integration and some functional analysis. Basic knowledge of Sobolev spaces would help, but is not necessary. The book can also serve as a reference for mathematicians working in the calculus of variations and partial differential equations as well as for researchers in other disciplines with a solid mathematics background. It contains several exercises and is self-contained.

Optimization in Solving Elliptic Problems

Author : Eugene G. D'yakonov
Publisher : CRC Press
ISBN 13 : 1351092111
Total Pages : 414 pages
Book Rating : 4.3/5 (51 download)

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Book Synopsis Optimization in Solving Elliptic Problems by : Eugene G. D'yakonov

Download or read book Optimization in Solving Elliptic Problems written by Eugene G. D'yakonov and published by CRC Press. This book was released on 2018-05-04 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization in Solving Elliptic Problems focuses on one of the most interesting and challenging problems of computational mathematics - the optimization of numerical algorithms for solving elliptic problems. It presents detailed discussions of how asymptotically optimal algorithms may be applied to elliptic problems to obtain numerical solutions meeting certain specified requirements. Beginning with an outline of the fundamental principles of numerical methods, this book describes how to construct special modifications of classical finite element methods such that for the arising grid systems, asymptotically optimal iterative methods can be applied. Optimization in Solving Elliptic Problems describes the construction of computational algorithms resulting in the required accuracy of a solution and having a pre-determined computational complexity. Construction of asymptotically optimal algorithms is demonstrated for multi-dimensional elliptic boundary value problems under general conditions. In addition, algorithms are developed for eigenvalue problems and Navier-Stokes problems. The development of these algorithms is based on detailed discussions of topics that include accuracy estimates of projective and difference methods, topologically equivalent grids and triangulations, general theorems on convergence of iterative methods, mixed finite element methods for Stokes-type problems, methods of solving fourth-order problems, and methods for solving classical elasticity problems. Furthermore, the text provides methods for managing basic iterative methods such as domain decomposition and multigrid methods. These methods, clearly developed and explained in the text, may be used to develop algorithms for solving applied elliptic problems. The mathematics necessary to understand the development of such algorithms is provided in the introductory material within the text, and common specifications of algorithms that have been developed for typical problems in mathema

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Author : Haim Brezis
Publisher : Springer Science & Business Media
ISBN 13 : 0387709142
Total Pages : 600 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Functional Analysis, Sobolev Spaces and Partial Differential Equations by : Haim Brezis

Download or read book Functional Analysis, Sobolev Spaces and Partial Differential Equations written by Haim Brezis and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.