Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces

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Publisher :
ISBN 13 : 9783030888572
Total Pages : 0 pages
Book Rating : 4.8/5 (885 download)

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Book Synopsis Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces by : Iwona Chlebicka

Download or read book Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces written by Iwona Chlebicka and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed study of nonlinear partial differential equations satisfying certain nonstandard growth conditions which simultaneously extend polynomial, inhomogeneous and fully anisotropic growth. The common property of the many different kinds of equations considered is that the growth conditions of the highest order operators lead to a formulation of the equations in Musielak-Orlicz spaces. This high level of generality, understood as full anisotropy and inhomogeneity, requires new proof concepts and a generalization of the formalism, calling for an extended functional analytic framework. This theory is established in the first part of the book, which serves as an introduction to the subject, but is also an important ingredient of the whole story. The second part uses these theoretical tools for various types of PDEs, including abstract and parabolic equations but also PDEs arising from fluid and solid mechanics. For connoisseurs, there is a short chapter on homogenization of elliptic PDEs. The book will be of interest to researchers working in PDEs and in functional analysis.

Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces

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Publisher : Springer Nature
ISBN 13 : 3030888568
Total Pages : 389 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces by : Iwona Chlebicka

Download or read book Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces written by Iwona Chlebicka and published by Springer Nature. This book was released on 2021-11-01 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed study of nonlinear partial differential equations satisfying certain nonstandard growth conditions which simultaneously extend polynomial, inhomogeneous and fully anisotropic growth. The common property of the many different kinds of equations considered is that the growth conditions of the highest order operators lead to a formulation of the equations in Musielak–Orlicz spaces. This high level of generality, understood as full anisotropy and inhomogeneity, requires new proof concepts and a generalization of the formalism, calling for an extended functional analytic framework. This theory is established in the first part of the book, which serves as an introduction to the subject, but is also an important ingredient of the whole story. The second part uses these theoretical tools for various types of PDEs, including abstract and parabolic equations but also PDEs arising from fluid and solid mechanics. For connoisseurs, there is a short chapter on homogenization of elliptic PDEs. The book will be of interest to researchers working in PDEs and in functional analysis.

Orlicz Spaces and Generalized Orlicz Spaces

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Publisher : Springer
ISBN 13 : 303015100X
Total Pages : 169 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Orlicz Spaces and Generalized Orlicz Spaces by : Petteri Harjulehto

Download or read book Orlicz Spaces and Generalized Orlicz Spaces written by Petteri Harjulehto and published by Springer. This book was released on 2019-05-07 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a technique centered on the use of equivalent Φ-functions. Results from classical functional analysis are presented in detail and new material is included on harmonic analysis. Extrapolation is used to prove, for example, the boundedness of Calderón–Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and Sobolev–Poincaré inequalities in norm and modular forms. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.

Handbook of Differential Equations: Stationary Partial Differential Equations

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Publisher : Elsevier
ISBN 13 : 0080463827
Total Pages : 631 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Handbook of Differential Equations: Stationary Partial Differential Equations by : Michel Chipot

Download or read book Handbook of Differential Equations: Stationary Partial Differential Equations written by Michel Chipot and published by Elsevier. This book was released on 2006-08-08 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Key features: - Written by well-known experts in the field- Self-contained volume in series covering one of the most rapid developing topics in mathematics - Written by well-known experts in the field- Self-contained volume in series covering one of the most rapid developing topics in mathematics

Partial Differential Equations with Variable Exponents

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Publisher : CRC Press
ISBN 13 : 1498703445
Total Pages : 321 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Partial Differential Equations with Variable Exponents by : Vicentiu D. Radulescu

Download or read book Partial Differential Equations with Variable Exponents written by Vicentiu D. Radulescu and published by CRC Press. This book was released on 2015-06-24 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational

Real-Variable Theory of Musielak-Orlicz Hardy Spaces

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Author :
Publisher : Springer
ISBN 13 : 331954361X
Total Pages : 476 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Real-Variable Theory of Musielak-Orlicz Hardy Spaces by : Dachun Yang

Download or read book Real-Variable Theory of Musielak-Orlicz Hardy Spaces written by Dachun Yang and published by Springer. This book was released on 2017-05-09 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of Musielak–Orlicz Hardy-type function spaces, and to lay the foundations for further applications. The real-variable theory of function spaces has always been at the core of harmonic analysis. Recently, motivated by certain questions in analysis, some more general Musielak–Orlicz Hardy-type function spaces were introduced. These spaces are defined via growth functions which may vary in both the spatial variable and the growth variable. By selecting special growth functions, the resulting spaces may have subtler and finer structures, which are necessary in order to solve various endpoint or sharp problems. This book is written for graduate students and researchers interested in function spaces and, in particular, Hardy-type spaces.

Lebesgue and Sobolev Spaces with Variable Exponents

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Publisher : Springer
ISBN 13 : 3642183638
Total Pages : 516 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Lebesgue and Sobolev Spaces with Variable Exponents by : Lars Diening

Download or read book Lebesgue and Sobolev Spaces with Variable Exponents written by Lars Diening and published by Springer. This book was released on 2011-03-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.

Partial Differential Equations

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Publisher : CRC Press
ISBN 13 : 9780203910108
Total Pages : 316 pages
Book Rating : 4.9/5 (11 download)

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Book Synopsis Partial Differential Equations by : Abdelmoujib Benkirane

Download or read book Partial Differential Equations written by Abdelmoujib Benkirane and published by CRC Press. This book was released on 2002-05-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This impressive compilation of the material presented at the International Conference on Partial Differential Equations held in Fez, Morocco, represents an integrated discussion of all major topics in the area of partial differential equations--highlighting recent progress and new trends for real-world applications.

Evolution PDEs with Nonstandard Growth Conditions

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Publisher : Springer
ISBN 13 : 9462391122
Total Pages : 417 pages
Book Rating : 4.4/5 (623 download)

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Book Synopsis Evolution PDEs with Nonstandard Growth Conditions by : Stanislav Antontsev

Download or read book Evolution PDEs with Nonstandard Growth Conditions written by Stanislav Antontsev and published by Springer. This book was released on 2015-04-01 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers the reader a treatment of the theory of evolution PDEs with nonstandard growth conditions. This class includes parabolic and hyperbolic equations with variable or anisotropic nonlinear structure. We develop methods for the study of such equations and present a detailed account of recent results. An overview of other approaches to the study of PDEs of this kind is provided. The presentation is focused on the issues of existence and uniqueness of solutions in appropriate function spaces and on the study of the specific qualitative properties of solutions, such as localization in space and time, extinction in a finite time and blow-up, or nonexistence of global in time solutions. Special attention is paid to the study of the properties intrinsic to solutions of equations with nonstandard growth.

Introduction to Partial Differential Equations

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Publisher : Springer Science & Business Media
ISBN 13 : 3319020994
Total Pages : 636 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Introduction to Partial Differential Equations by : Peter J. Olver

Download or read book Introduction to Partial Differential Equations written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2013-11-08 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.

Morrey Spaces

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Publisher : CRC Press
ISBN 13 : 1000064077
Total Pages : 316 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Morrey Spaces by : Yoshihiro Sawano

Download or read book Morrey Spaces written by Yoshihiro Sawano and published by CRC Press. This book was released on 2020-09-16 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused mainly generalizations and interpolation of Morrey spaces. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

Seminar of Mathematical Analysis

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Publisher : Universidad de Sevilla
ISBN 13 : 9788447208036
Total Pages : 282 pages
Book Rating : 4.2/5 (8 download)

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Book Synopsis Seminar of Mathematical Analysis by : Genaro (ed.) L"pez Acedo

Download or read book Seminar of Mathematical Analysis written by Genaro (ed.) L"pez Acedo and published by Universidad de Sevilla. This book was released on 2003 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ponencias de los seminarios de análisis matemáticos impartidos en Málaga y Sevilla entre septiembre de 2002 y febrero de 2003. Entre los diversos artículos que contiene citamos: Continuous descent methods, Algebras of analytic functions on Banach Spaces; también en español como Estimaciones con peso deducidas del Principio de Calderón-Zygmund, etc.

Function Spaces and Partial Differential Equations

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Publisher : Oxford Lecture Mathematics and
ISBN 13 : 0198733135
Total Pages : 523 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 523 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.

More Progresses in Analysis

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Author :
Publisher : World Scientific
ISBN 13 : 9812835636
Total Pages : 1497 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis More Progresses in Analysis by :

Download or read book More Progresses in Analysis written by and published by World Scientific. This book was released on 2009-05-12 with total page 1497 pages. Available in PDF, EPUB and Kindle. Book excerpt: International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors. The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O. Besov, V. Burenkov and R.P. Gilbert on the occasion of their anniversaries.

More Progresses in Analysis

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Author :
Publisher : World Scientific
ISBN 13 : 9812835628
Total Pages : 1497 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis More Progresses in Analysis by : Heinrich G. W. Begehr

Download or read book More Progresses in Analysis written by Heinrich G. W. Begehr and published by World Scientific. This book was released on 2009 with total page 1497 pages. Available in PDF, EPUB and Kindle. Book excerpt: International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors. The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O Besov, V Burenkov and R P Gilbert on the occasion of their anniversaries.

More Progresses In Analysis - Proceedings Of The 5th International Isaac Congress

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Publisher : World Scientific
ISBN 13 : 9814469688
Total Pages : 1497 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis More Progresses In Analysis - Proceedings Of The 5th International Isaac Congress by : Heinrich G W Begehr

Download or read book More Progresses In Analysis - Proceedings Of The 5th International Isaac Congress written by Heinrich G W Begehr and published by World Scientific. This book was released on 2009-05-12 with total page 1497 pages. Available in PDF, EPUB and Kindle. Book excerpt: International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors.The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O Besov, V Burenkov and R P Gilbert on the occasion of their anniversaries.

Nine Papers on Partial Differential Equations and Functional Analysis

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 9780821896419
Total Pages : 316 pages
Book Rating : 4.8/5 (964 download)

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Book Synopsis Nine Papers on Partial Differential Equations and Functional Analysis by :

Download or read book Nine Papers on Partial Differential Equations and Functional Analysis written by and published by American Mathematical Soc.. This book was released on 1967-12-31 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: