A First Course In Sobolev Spaces

Author : Giovanni Leoni
Publisher : American Mathematical Soc.
Page : 626 pages
File Size : 46,7 Mb
Release : 2009
Category : Sobolev spaces
ISBN : 9780821847688

Get Book

A First Course in Sobolev Spaces by Giovanni Leoni Pdf

Sobolev spaces are a fundamental tool in the modern study of partial differential equations. In this book, Leoni takes a novel approach to the theory by looking at Sobolev spaces as the natural development of monotone, absolutely continuous, and BV functions of one variable. In this way, the majority of the text can be read without the prerequisite of a course in functional analysis. The first part of this text is devoted to studying functions of one variable. Several of the topics treated occur in courses on real analysis or measure theory. Here, the perspective emphasizes their applications to Sobolev functions, giving a very different flavor to the treatment. This elementary start to the book makes it suitable for advanced undergraduates or beginning graduate students. Moreover, the one-variable part of the book helps to develop a solid background that facilitates the reading and understanding of Sobolev functions of several variables. The second part of the book is more classical, although it also contains some recent results. Besides the standard results on Sobolev functions, this part of the book includes chapters on BV functions, symmetric rearrangement, and Besov spaces. The book contains over 200 exercises.

Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 42,9 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9780387709147

Get Book

Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis Pdf

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.

Author : Nikolaĭ Vladimirovich Krylov
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 44,5 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821805695

Get Book

Lectures on Elliptic and Parabolic Equations in Hölder Spaces by Nikolaĭ Vladimirovich Krylov Pdf

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.

Author : Lars Diening,Petteri Harjulehto,Peter Hästö,Michael Ruzicka
Publisher : Springer
Page : 509 pages
File Size : 49,9 Mb
Release : 2011-03-29
Category : Mathematics
ISBN : 9783642183638

Get Book

Lebesgue and Sobolev Spaces with Variable Exponents by Lars Diening,Petteri Harjulehto,Peter Hästö,Michael Ruzicka Pdf

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.

Author : Juha Heinonen,Pekka Koskela,Nageswari Shanmugalingam,Jeremy T. Tyson
Publisher : Cambridge University Press
Page : 447 pages
File Size : 43,8 Mb
Release : 2015-02-05
Category : Mathematics
ISBN : 9781107092341

Get Book

Sobolev Spaces on Metric Measure Spaces by Juha Heinonen,Pekka Koskela,Nageswari Shanmugalingam,Jeremy T. Tyson Pdf

This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.

Author : Irene Fonseca,Giovanni Leoni
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 54,8 Mb
Release : 2007-08-22
Category : Science
ISBN : 9780387690063

Get Book

Modern Methods in the Calculus of Variations by Irene Fonseca,Giovanni Leoni Pdf

This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.

Author : Nikolaĭ Vladimirovich Krylov
Publisher : American Mathematical Soc.
Page : 377 pages
File Size : 46,8 Mb
Release : 2008
Category : Differential equations, Elliptic
ISBN : 9780821846841

Get Book

Lectures on Elliptic and Parabolic Equations in Sobolev Spaces by Nikolaĭ Vladimirovich Krylov Pdf

This book concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces. The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations. In addition, other boundary-value problems such as the Neumann or oblique derivative problems are briefly covered. As is natural for a textbook, the main emphasis is on organizing well-known ideas in a self-contained exposition. Among the topics included that are not usually covered in a textbook are a relatively recent development concerning equations with $\textsf{VMO}$ coefficients and the study of parabolic equations with coefficients measurable only with respect to the time variable. There are numerous exercises which help the reader better understand the material. After going through the book, the reader will have a good understanding of results available in the modern theory of partial differential equations and the technique used to obtain them. Prerequesites are basics of measure theory, the theory of $L p$ spaces, and the Fourier transform.

Author : Dominic Breit,Franz Gmeineder
Publisher : Springer
Page : 0 pages
File Size : 55,7 Mb
Release : 2023-02-06
Category : Mathematics
ISBN : 3030806421

Get Book

A Course on Function Spaces by Dominic Breit,Franz Gmeineder Pdf

This textbook provides a thorough-yet-accessible introduction to function spaces, through the central concepts of integrability, weakly differentiability and fractionally differentiability. In an essentially self-contained treatment the reader is introduced to Lebesgue, Sobolev and BV-spaces, before being guided through various generalisations such as Bessel-potential spaces, fractional Sobolev spaces and Besov spaces. Written with the student in mind, the book gradually proceeds from elementary properties to more advanced topics such as lower dimensional trace embeddings, fine properties and approximate differentiability, incorporating recent approaches. Throughout, the authors provide careful motivation for the underlying concepts, which they illustrate with selected applications from partial differential equations, demonstrating the relevance and practical use of function spaces. Assuming only multivariable calculus and elementary functional analysis, as conveniently summarised in the opening chapters, A Course in Function Spaces is designed for lecture courses at the graduate level and will also be a valuable companion for young researchers in analysis.

Author : Hans Triebel
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 41,7 Mb
Release : 2010-05-18
Category : Science
ISBN : 9783034604192

Get Book

Theory of Function Spaces II by Hans Triebel Pdf

Author : Vladimir I. Bogachev,Oleg G. Smolyanov
Publisher : Springer Nature
Page : 586 pages
File Size : 52,8 Mb
Release : 2020-02-25
Category : Mathematics
ISBN : 9783030382193

Get Book

Real and Functional Analysis by Vladimir I. Bogachev,Oleg G. Smolyanov Pdf

This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.

Author : Giovanni Leoni
Publisher : American Mathematical Society
Page : 759 pages
File Size : 43,9 Mb
Release : 2024-04-17
Category : Mathematics
ISBN : 9781470477028

Get Book

A First Course in Sobolev Spaces by Giovanni Leoni Pdf

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.

Author : Juha Heinonen
Publisher : Springer Science & Business Media
Page : 149 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461301318

Get Book

Lectures on Analysis on Metric Spaces by Juha Heinonen Pdf

The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is recent and appears for the first time in book format.

Author : James C. Robinson
Publisher : Cambridge University Press
Page : 488 pages
File Size : 50,7 Mb
Release : 2001-04-23
Category : Mathematics
ISBN : 0521632048

Get Book

Infinite-Dimensional Dynamical Systems by James C. Robinson Pdf

This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject. As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems. Since the subject is relatively new, this is the first book to attempt to treat these various topics in a unified and didactic way. It is intended to be suitable for first year graduate students.

Author : Robert A. Adams,John J. F. Fournier
Publisher : Elsevier
Page : 320 pages
File Size : 48,5 Mb
Release : 2003-06-26
Category : Mathematics
ISBN : 0080541291

Get Book

Sobolev Spaces by Robert A. Adams,John J. F. Fournier Pdf

Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences. This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike. Self-contained and accessible for readers in other disciplines Written at elementary level making it accessible to graduate students

Author : John B Conway
Publisher : Springer
Page : 416 pages
File Size : 42,7 Mb
Release : 2019-03-09
Category : Mathematics
ISBN : 9781475743838

Get Book

A Course in Functional Analysis by John B Conway Pdf

This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general. From the reviews: "This book is an excellent text for a first graduate course in functional analysis....Many interesting and important applications are included....It includes an abundance of exercises, and is written in the engaging and lucid style which we have come to expect from the author." --MATHEMATICAL REVIEWS