A First Course In Sobolev Spaces

Author : Giovanni Leoni
Publisher : American Mathematical Soc.
ISBN 13 : 0821847686
Total Pages : 626 pages
Book Rating : 4.88/5 ( download)

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Download or read book A First Course in Sobolev Spaces written by Giovanni Leoni and published by American Mathematical Soc.. This book was released on 2009 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Giovanni Leoni
Publisher : American Mathematical Soc.
ISBN 13 : 0821884158
Total Pages : 626 pages
Book Rating : 4.57/5 ( download)

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Download or read book A First Course in Sobolev Spaces written by Giovanni Leoni and published by American Mathematical Soc.. This book was released on 2009-01-01 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."--P. [4] de la couv.

Author : Giovanni Leoni
Publisher :
ISBN 13 : 9781470411695
Total Pages : 626 pages
Book Rating : 4.95/5 ( download)

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Download or read book A First Course in Sobolev Spaces written by Giovanni Leoni and published by . This book was released on 2009 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Haim Brezis
Publisher : Springer Science & Business Media
ISBN 13 : 0387709142
Total Pages : 600 pages
Book Rating : 4.47/5 ( download)

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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.

Author : Nikolaĭ Vladimirovich Krylov
Publisher : American Mathematical Soc.
ISBN 13 : 0821846841
Total Pages : 377 pages
Book Rating : 4.41/5 ( download)

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Download or read book Lectures on Elliptic and Parabolic Equations in Sobolev Spaces written by Nikolaĭ Vladimirovich Krylov and published by American Mathematical Soc.. This book was released on 2008 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Nikolaĭ Vladimirovich Krylov
Publisher : American Mathematical Soc.
ISBN 13 : 082180569X
Total Pages : 164 pages
Book Rating : 4.95/5 ( download)

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Download or read book Lectures on Elliptic and Parabolic Equations in Hölder Spaces written by Nikolaĭ Vladimirovich Krylov and published by American Mathematical Soc.. This book was released on 1996 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer
ISBN 13 : 3642183638
Total Pages : 509 pages
Book Rating : 4.38/5 ( download)

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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 509 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.

Author : Hans Triebel
Publisher : Springer Science & Business Media
ISBN 13 : 303460419X
Total Pages : 376 pages
Book Rating : 4.92/5 ( download)

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Download or read book Theory of Function Spaces II written by Hans Triebel and published by Springer Science & Business Media. This book was released on 2010-05-18 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Juha Heinonen
Publisher : Cambridge University Press
ISBN 13 : 1107092345
Total Pages : 447 pages
Book Rating : 4.41/5 ( download)

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Download or read book Sobolev Spaces on Metric Measure Spaces written by Juha Heinonen and published by Cambridge University Press. This book was released on 2015-02-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.

Author : John B Conway
Publisher : Springer
ISBN 13 : 1475743831
Total Pages : 416 pages
Book Rating : 4.38/5 ( download)

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Download or read book A Course in Functional Analysis written by John B Conway and published by Springer. This book was released on 2019-03-09 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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