Partial Differential Equations In Sobolev And Analytic Spaces
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Functional Analysis Sobolev Spaces And Partial Differential Equations
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Author : Haim Brezis
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-10
Functional Analysis Sobolev Spaces And Partial Differential Equations written by Haim Brezis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-10 with Mathematics categories.
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.
Sobolev Spaces
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Author : Vladimir Maz'ya
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-11
Sobolev Spaces written by Vladimir Maz'ya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-11 with Mathematics categories.
Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume first appeared in German as three booklets of Teubner-Texte zur Mathematik (1979, 1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a significantly augmented list of references aim to create a broader and modern view of the area.
Partial Diffrential Equations In Sobolev And Analytic Spaces
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Author : GEORGIEV
language : en
Publisher: World Scientific Publishing Company
Release Date : 2025-02-07
Partial Diffrential Equations In Sobolev And Analytic Spaces written by GEORGIEV and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-07 with Mathematics categories.
Partial Differential Equations (PDEs) are fundamental in fields such as physics and engineering, underpinning our understanding of sound, heat, diffusion, electrostatics, electrodynamics, thermodynamics, fluid dynamics, elasticity, general relativity, and quantum mechanics. They also arise in areas like differential geometry and the calculus of variations.This book focuses on recent investigations of PDEs in Sobolev and analytic spaces. It consists of twelve chapters, starting with foundational definitions and results on linear, metric, normed, and Banach spaces, which are essential for introducing weak solutions to PDEs. Subsequent chapters cover topics such as Lebesgue integration, Lp spaces, distributions, Fourier transforms, Sobolev and Bourgain spaces, and various types of KdV equations. Advanced topics include higher order dispersive equations, local and global well-posedness, and specific classes of Kadomtsev-Petviashvili equations.This book is intended for specialists like mathematicians, physicists, engineers, and biologists. It can serve as a graduate-level textbook and a reference for multiple disciplines.
Functional Spaces For The Theory Of Elliptic Partial Differential Equations
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Author : Françoise Demengel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-24
Functional Spaces For The Theory Of Elliptic Partial Differential Equations written by Françoise Demengel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-24 with Mathematics categories.
The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions. This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem. The main purpose of the book is to provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on the Schwartz space. There are complete and detailed proofs of almost all the results announced and, in some cases, more than one proof is provided in order to highlight different features of the result. Each chapter concludes with a range of exercises of varying levels of difficulty, with hints to solutions provided for many of them.
Sobolev Spaces
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Author : Vladimir Maz'ya
language : en
Publisher: Springer
Release Date : 2013-12-21
Sobolev Spaces written by Vladimir Maz'ya and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-21 with Mathematics categories.
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
A First Course In Sobolev Spaces
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Author : Giovanni Leoni
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-17
A First Course In Sobolev Spaces written by Giovanni Leoni and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-17 with Mathematics categories.
This book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate course in functions of one variable and one for a graduate course on Sobolev functions. The first part develops the theory of monotone, absolutely continuous, and bounded variation functions of one variable and their relationship with Lebesgue–Stieltjes measures and Sobolev functions. It also studies decreasing rearrangement and curves. The second edition includes a chapter on functions mapping time into Banach spaces. The second part of the book studies functions of several variables. It begins with an overview of classical results such as Rademacher's and Stepanoff's differentiability theorems, Whitney's extension theorem, Brouwer's fixed point theorem, and the divergence theorem for Lipschitz domains. It then moves to distributions, Fourier transforms and tempered distributions. The remaining chapters are a treatise on Sobolev functions. The second edition focuses more on higher order derivatives and it includes the interpolation theorems of Gagliardo and Nirenberg. It studies embedding theorems, extension domains, chain rule, superposition, Poincaré's inequalities and traces. A major change compared to the first edition is the chapter on Besov spaces, which are now treated using interpolation theory.
Lectures On Elliptic And Parabolic Equations In Holder Spaces
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Author : Nikolaĭ Vladimirovich Krylov
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Lectures On Elliptic And Parabolic Equations In Holder Spaces written by Nikolaĭ Vladimirovich Krylov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in H older spaces. Krylov shows that this theory - including some issues of the theory of nonlinear equations - is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed. This book, containing 200 exercises, aims to provide a good understanding of what kind of results are available and what kinds of techniques are used to obtain them.
An Introduction To Partial Differential Equations
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Author : Michael Renardy
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
An Introduction To Partial Differential Equations written by Michael Renardy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-18 with Mathematics categories.
Partial differential equations are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis and algebraic topology. Like algebra, topology, and rational mechanics, partial differential equations are a core area of mathematics. This book aims to provide the background necessary to initiate work on a Ph.D. thesis in PDEs for beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables. Lebesgue integration is needed only in Chapter 10, and the necessary tools from functional analysis are developed within the course. The book can be used to teach a variety of different courses. This new edition features new problems throughout and the problems have been rearranged in each section from simplest to most difficult. New examples have also been added. The material on Sobolev spaces has been rearranged and expanded. A new section on nonlinear variational problems with "Young-measure" solutions appears. The reference section has also been expanded.
Sobolev Spaces Of Fractional Order Nemytskij Operators And Nonlinear Partial Differential Equations
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Author : Thomas Runst
language : en
Publisher: Walter de Gruyter
Release Date : 2011-07-22
Sobolev Spaces Of Fractional Order Nemytskij Operators And Nonlinear Partial Differential Equations written by Thomas Runst and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-22 with Mathematics categories.
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. Please submit book proposals to Jürgen Appell.
Fourier Analysis And Partial Differential Equations
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Author : Iorio Júnior Iorio Jr.
language : en
Publisher: Cambridge University Press
Release Date : 2001-03-15
Fourier Analysis And Partial Differential Equations written by Iorio Júnior Iorio Jr. and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-15 with Mathematics categories.
This book was first published in 2001. It provides an introduction to Fourier analysis and partial differential equations and is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations. The first part of the book consists of some very classical material, followed by a discussion of the theory of periodic distributions and the periodic Sobolev spaces. The authors then turn to the study of linear and nonlinear equations in the setting provided by periodic distributions. They assume only some familiarity with Banach and Hilbert spaces and the elementary properties of bounded linear operators. After presenting a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations, they turn their attention, in the two final chapters, to the non-periodic setting, concentrating on problems that do not occur in the periodic case.