A First Course In Sobolev Spaces PDF Download
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Author | : Giovanni Leoni |
Publisher | : American Mathematical Soc. |
Total Pages | : 626 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0821847686 |
Download A First Course in Sobolev Spaces Book in PDF, ePub and Kindle
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. |
Total Pages | : 626 |
Release | : 2009-01-01 |
Genre | : Mathematics |
ISBN | : 0821884158 |
Download A First Course in Sobolev Spaces Book in PDF, ePub and Kindle
"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 | : |
Total Pages | : 626 |
Release | : 2009 |
Genre | : Sobolev spaces |
ISBN | : 9781470411695 |
Download A First Course in Sobolev Spaces Book in PDF, ePub and Kindle
Author | : Haim Brezis |
Publisher | : Springer Science & Business Media |
Total Pages | : 600 |
Release | : 2010-11-02 |
Genre | : Mathematics |
ISBN | : 0387709142 |
Download Functional Analysis, Sobolev Spaces and Partial Differential Equations Book in PDF, ePub and Kindle
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. |
Total Pages | : 178 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 082180569X |
Download Lectures on Elliptic and Parabolic Equations in Holder Spaces Book in PDF, ePub and Kindle
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 | : Nikolaĭ Vladimirovich Krylov |
Publisher | : American Mathematical Soc. |
Total Pages | : 377 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821846841 |
Download Lectures on Elliptic and Parabolic Equations in Sobolev Spaces Book in PDF, ePub and Kindle
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 | : Lars Diening |
Publisher | : Springer |
Total Pages | : 516 |
Release | : 2011-03-29 |
Genre | : Mathematics |
ISBN | : 3642183638 |
Download Lebesgue and Sobolev Spaces with Variable Exponents Book in PDF, ePub and Kindle
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 | : Eugenio Hernandez |
Publisher | : CRC Press |
Total Pages | : 518 |
Release | : 1996-09-12 |
Genre | : Mathematics |
ISBN | : 9781420049985 |
Download A First Course on Wavelets Book in PDF, ePub and Kindle
Wavelet theory had its origin in quantum field theory, signal analysis, and function space theory. In these areas wavelet-like algorithms replace the classical Fourier-type expansion of a function. This unique new book is an excellent introduction to the basic properties of wavelets, from background math to powerful applications. The authors provide elementary methods for constructing wavelets, and illustrate several new classes of wavelets. The text begins with a description of local sine and cosine bases that have been shown to be very effective in applications. Very little mathematical background is needed to follow this material. A complete treatment of band-limited wavelets follows. These are characterized by some elementary equations, allowing the authors to introduce many new wavelets. Next, the idea of multiresolution analysis (MRA) is developed, and the authors include simplified presentations of previous studies, particularly for compactly supported wavelets. Some of the topics treated include: Several bases generated by a single function via translations and dilations Multiresolution analysis, compactly supported wavelets, and spline wavelets Band-limited wavelets Unconditionality of wavelet bases Characterizations of many of the principal objects in the theory of wavelets, such as low-pass filters and scaling functions The authors also present the basic philosophy that all orthonormal wavelets are completely characterized by two simple equations, and that most properties and constructions of wavelets can be developed using these two equations. Material related to applications is provided, and constructions of splines wavelets are presented. Mathematicians, engineers, physicists, and anyone with a mathematical background will find this to be an important text for furthering their studies on wavelets.
Author | : Juha Heinonen |
Publisher | : Cambridge University Press |
Total Pages | : 447 |
Release | : 2015-02-05 |
Genre | : Mathematics |
ISBN | : 1107092345 |
Download Sobolev Spaces on Metric Measure Spaces Book in PDF, ePub and Kindle
This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.
Author | : Alberto Bressan |
Publisher | : American Mathematical Soc. |
Total Pages | : 265 |
Release | : 2013 |
Genre | : Mathematics |
ISBN | : 0821887718 |
Download Lecture Notes on Functional Analysis Book in PDF, ePub and Kindle
This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations. The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra. The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.