Beyond Sobolev And Besov PDF Download
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Author | : Cornelia Schneider |
Publisher | : Springer Nature |
Total Pages | : 339 |
Release | : 2021-05-31 |
Genre | : Mathematics |
ISBN | : 3030751392 |
Download Beyond Sobolev and Besov Book in PDF, ePub and Kindle
This book investigates the close relation between quite sophisticated function spaces, the regularity of solutions of partial differential equations (PDEs) in these spaces and the link with the numerical solution of such PDEs. It consists of three parts. Part I, the introduction, provides a quick guide to function spaces and the general concepts needed. Part II is the heart of the monograph and deals with the regularity of solutions in Besov and fractional Sobolev spaces. In particular, it studies regularity estimates of PDEs of elliptic, parabolic and hyperbolic type on non smooth domains. Linear as well as nonlinear equations are considered and special attention is paid to PDEs of parabolic type. For the classes of PDEs investigated a justification is given for the use of adaptive numerical schemes. Finally, the last part has a slightly different focus and is concerned with traces in several function spaces such as Besov– and Triebel–Lizorkin spaces, but also in quite general smoothness Morrey spaces. The book is aimed at researchers and graduate students working in regularity theory of PDEs and function spaces, who are looking for a comprehensive treatment of the above listed topics.
Author | : Giovanni Leoni |
Publisher | : American Mathematical Society |
Total Pages | : 759 |
Release | : 2024-04-17 |
Genre | : Mathematics |
ISBN | : 1470477025 |
Download A First Course in Sobolev Spaces Book in PDF, ePub and Kindle
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 | : 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 | : 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 | : Bin Han |
Publisher | : Springer |
Total Pages | : 750 |
Release | : 2018-01-04 |
Genre | : Mathematics |
ISBN | : 3319685309 |
Download Framelets and Wavelets Book in PDF, ePub and Kindle
Marking a distinct departure from the perspectives of frame theory and discrete transforms, this book provides a comprehensive mathematical and algorithmic introduction to wavelet theory. As such, it can be used as either a textbook or reference guide. As a textbook for graduate mathematics students and beginning researchers, it offers detailed information on the basic theory of framelets and wavelets, complemented by self-contained elementary proofs, illustrative examples/figures, and supplementary exercises. Further, as an advanced reference guide for experienced researchers and practitioners in mathematics, physics, and engineering, the book addresses in detail a wide range of basic and advanced topics (such as multiwavelets/multiframelets in Sobolev spaces and directional framelets) in wavelet theory, together with systematic mathematical analysis, concrete algorithms, and recent developments in and applications of framelets and wavelets. Lastly, the book can also be used to teach on or study selected special topics in approximation theory, Fourier analysis, applied harmonic analysis, functional analysis, and wavelet-based signal/image processing.
Author | : Kalle Åström |
Publisher | : Springer Science & Business Media |
Total Pages | : 355 |
Release | : 2012-01-05 |
Genre | : Mathematics |
ISBN | : 3642202365 |
Download Analysis for Science, Engineering and Beyond Book in PDF, ePub and Kindle
This book project was initiated at The Tribute Workshop in Honour of Gunnar Sparr and the follow-up workshop Inequalities, Interpolation, Non-commutative, Analysis, Non-commutative Geometry and Applications INANGA08, held at the Centre for Mathematical Sciences, Lund University in May and November of 2008. The resulting book is dedicated in celebration of Gunnar Sparr's sixty-fifth anniversary and more than forty years of exceptional service to mathematics and its applications in engineering and technology, mathematics and engineering education, as well as interdisciplinary, industrial and international cooperation. This book presents new advances in several areas of mathematics and engineering mathematics including applications in modern technology, engineering and life sciences. Thirteen high-quality chapters put forward many new methods and results, reviews of up to date research and open directions and problems for future research. A special chapter by Gunnar Sparr and Georg Lindgren contains a historical account and important aspects of engineering mathematics research and education, and the implementation of the highly successful education programme in Engineering Mathematics at Lund Institute of Technology, where not only the mathematical sciences have played a role. This book will serve as a source of inspiration for a broad spectrum of researchers and research students.
Author | : Sabir Umarov |
Publisher | : World Scientific |
Total Pages | : 192 |
Release | : 2018-02-13 |
Genre | : Mathematics |
ISBN | : 9813230991 |
Download Beyond The Triangle: Brownian Motion, Ito Calculus, And Fokker-planck Equation - Fractional Generalizations Book in PDF, ePub and Kindle
The book is devoted to the fundamental relationship between three objects: a stochastic process, stochastic differential equations driven by that process and their associated Fokker-Planck-Kolmogorov equations. This book discusses wide fractional generalizations of this fundamental triple relationship, where the driving process represents a time-changed stochastic process; the Fokker-Planck-Kolmogorov equation involves time-fractional order derivatives and spatial pseudo-differential operators; and the associated stochastic differential equation describes the stochastic behavior of the solution process. It contains recent results obtained in this direction.This book is important since the latest developments in the field, including the role of driving processes and their scaling limits, the forms of corresponding stochastic differential equations, and associated FPK equations, are systematically presented. Examples and important applications to various scientific, engineering, and economics problems make the book attractive for all interested researchers, educators, and graduate students.
Author | : |
Publisher | : |
Total Pages | : 458 |
Release | : 1985 |
Genre | : Numerical analysis |
ISBN | : |
Download Publications du Laboratoire d'analyse numérique Book in PDF, ePub and Kindle
Author | : Hassane Bougrini |
Publisher | : Nova Publishers |
Total Pages | : 122 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9781560728788 |
Download Symbolic Calculus Semilinear Hyperbolic Progressing Waves Book in PDF, ePub and Kindle
The main purpose of this book is to give a self-contained synthesis of different results in the domain of symbolic calculus of conormal singularities of semilinear hyperbolic progressing waves. The authors deal generally with real matrix valued co-efficients and with real vector valued solutions, but the complex case is similar. They consider also N x N first order systems rather than high order scalar equations, because the polarisation properties of symbols are less natural in the latter case. Moreover, although they assume generally that the real characteristics are simple, the methods can give results for symmetric or symmetrisable first order hyperbolic systems.
Author | : Juan Gil |
Publisher | : Birkhäuser |
Total Pages | : 574 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034878508 |
Download Aspects of Boundary Problems in Analysis and Geometry Book in PDF, ePub and Kindle
Boundary problems constitute an essential field of common mathematical interest, they lie in the center of research activities both in analysis and geometry. This book encompasses material from both disciplines, and focuses on their interactions which are particularly apparent in this field. Moreover, the survey style of the contributions makes the topics accessible to a broad audience with a background in analysis or geometry, and enables the reader to get a quick overview.