Fine Regularity Of Solutions Of Elliptic Partial Differential Equations

Author : Jan Malý
Publisher : American Mathematical Soc.
ISBN 13 : 0821803352
Total Pages : 309 pages
Book Rating : 4.56/5 ( download)

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Download or read book Fine Regularity of Solutions of Elliptic Partial Differential Equations written by Jan Malý and published by American Mathematical Soc.. This book was released on 1997 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary objective of this monograph is to give a comprehensive exposition of results surrounding the work of the authors concerning boundary regularity of weak solutions of second order elliptic quasilinear equations in divergence form. The book also contains a complete development of regularity of solutions of variational inequalities, including the double obstacle problem, where the obstacles are allowed to be discontinuous. The book concludes with a chapter devoted to the existence theory thus providing the reader with a complete treatment of the subject ranging from regularity of weak solutions to the existence of weak solutions.

Author : Louis Dupaigne
Publisher : CRC Press
ISBN 13 : 1420066544
Total Pages : 337 pages
Book Rating : 4.48/5 ( download)

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Download or read book Stable Solutions of Elliptic Partial Differential Equations written by Louis Dupaigne and published by CRC Press. This book was released on 2011-03-15 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfaces). Stable Solutions of Elliptic Partial Differential Equations offers a self-contained presentation of the notion of stability in elliptic partial differential equations (PDEs). The central questions of regularity and classification of stable solutions are treated at length. Specialists will find a summary of the most recent developments of the theory, such as nonlocal and higher-order equations. For beginners, the book walks you through the fine versions of the maximum principle, the standard regularity theory for linear elliptic equations, and the fundamental functional inequalities commonly used in this field. The text also includes two additional topics: the inverse-square potential and some background material on submanifolds of Euclidean space.

Author : Lucio Boccardo
Publisher : Walter de Gruyter
ISBN 13 : 3110315424
Total Pages : 204 pages
Book Rating : 4.24/5 ( download)

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Download or read book Elliptic Partial Differential Equations written by Lucio Boccardo and published by Walter de Gruyter. This book was released on 2013-10-29 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elliptic partial differential equations is one of the main and most active areas in mathematics. This book is devoted to the study of linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments about distributional solutions. For this reason this monograph is addressed to master's students, PhD students and anyone who wants to begin research in this mathematical field.

Author : Lisa Beck
Publisher : Springer
ISBN 13 : 3319274856
Total Pages : 201 pages
Book Rating : 4.50/5 ( download)

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Download or read book Elliptic Regularity Theory written by Lisa Beck and published by Springer. This book was released on 2016-04-08 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of some classical results on everywhere regularity for scalar-valued weak solutions, the presentation focuses on vector-valued weak solutions to a system of several coupled equations. In the vectorial case, weak solutions may have discontinuities and so are expected, in general, to be regular only outside of a set of measure zero. Several methods are presented concerning the proof of such partial regularity results, and optimal regularity is discussed. Finally, a short overview is given on the current state of the art concerning the size of the singular set on which discontinuities may occur. The notes are intended for graduate and postgraduate students with a solid background in functional analysis and some familiarity with partial differential equations; they will also be of interest to researchers working on related topics.

Author : David Gilbarg
Publisher : Springer Science & Business Media
ISBN 13 : 9783540411604
Total Pages : 544 pages
Book Rating : 4.07/5 ( download)

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Download or read book Elliptic Partial Differential Equations of Second Order written by David Gilbarg and published by Springer Science & Business Media. This book was released on 2001-01-12 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work aims to be of interest to those who have to work with differential equations and acts either as a reference or as a book to learn from. The authors have made the treatment self-contained.

Author : Charles B. Morrey
Publisher : American Mathematical Soc.
ISBN 13 : 0821814044
Total Pages : 177 pages
Book Rating : 4.48/5 ( download)

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Download or read book Partial Differential Equations written by Charles B. Morrey and published by American Mathematical Soc.. This book was released on 1961 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Luis Angel Caffarelli
Publisher : Edizioni della Normale
ISBN 13 : 9788876422492
Total Pages : 0 pages
Book Rating : 4.98/5 ( download)

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Download or read book The obstacle problem written by Luis Angel Caffarelli and published by Edizioni della Normale. This book was released on 1999-10-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material presented here corresponds to Fermi lectures that I was invited to deliver at the Scuola Normale di Pisa in the spring of 1998. The obstacle problem consists in studying the properties of minimizers of the Dirichlet integral in a domain D of Rn, among all those configurations u with prescribed boundary values and costrained to remain in D above a prescribed obstacle F. In the Hilbert space H1(D) of all those functions with square integrable gradient, we consider the closed convex set K of functions u with fixed boundary value and which are greater than F in D. There is a unique point in K minimizing the Dirichlet integral. That is called the solution to the obstacle problem.

Author : Ya-Zhe Chen
Publisher : American Mathematical Soc.
ISBN 13 : 0821819240
Total Pages : 266 pages
Book Rating : 4.41/5 ( download)

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Download or read book Second Order Elliptic Equations and Elliptic Systems written by Ya-Zhe Chen and published by American Mathematical Soc.. This book was released on 1998 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are two parts to the book. In the first part, a complete introduction of various kinds of a priori estimate methods for the Dirichlet problem of second order elliptic partial differential equations is presented. In the second part, the existence and regularity theories of the Dirichlet problem for linear and nonlinear second order elliptic partial differential systems are introduced. The book features appropriate materials and is an excellent textbook for graduate students. The volume is also useful as a reference source for undergraduate mathematics majors, graduate students, professors, and scientists.

Author : Ariel Barton
Publisher : American Mathematical Soc.
ISBN 13 : 0821887408
Total Pages : 120 pages
Book Rating : 4.00/5 ( download)

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Download or read book Elliptic Partial Differential Equations with Almost-Real Coefficients written by Ariel Barton and published by American Mathematical Soc.. This book was released on 2013-04-22 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph the author investigates divergence-form elliptic partial differential equations in two-dimensional Lipschitz domains whose coefficient matrices have small (but possibly nonzero) imaginary parts and depend only on one of the two coordinates. He shows that for such operators, the Dirichlet problem with boundary data in $L^q$ can be solved for $q1$ small enough, and provide an endpoint result at $p=1$.

Author : Walter A. Strauss
Publisher : John Wiley & Sons
ISBN 13 : 0470054565
Total Pages : 467 pages
Book Rating : 4.67/5 ( download)

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Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.