Nonlinear Potential Theory of Degenerate Elliptic Equations
Title | Nonlinear Potential Theory of Degenerate Elliptic Equations PDF eBook |
Author | Juha Heinonen |
Publisher | Courier Dover Publications |
Total Pages | 416 |
Release | 2018-05-16 |
Genre | Mathematics |
ISBN | 0486830462 |
A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. 1993 edition.
Nonlinear Potential Theory and Weighted Sobolev Spaces
Title | Nonlinear Potential Theory and Weighted Sobolev Spaces PDF eBook |
Author | Bengt O. Turesson |
Publisher | Springer |
Total Pages | 188 |
Release | 2007-05-06 |
Genre | Mathematics |
ISBN | 3540451684 |
The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.
Potential Theory - ICPT 94
Title | Potential Theory - ICPT 94 PDF eBook |
Author | Josef Kral |
Publisher | Walter de Gruyter |
Total Pages | 513 |
Release | 2011-10-13 |
Genre | Mathematics |
ISBN | 3110818574 |
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Moduli in Modern Mapping Theory
Title | Moduli in Modern Mapping Theory PDF eBook |
Author | Olli Martio |
Publisher | Springer Science & Business Media |
Total Pages | 368 |
Release | 2008-11-09 |
Genre | Mathematics |
ISBN | 0387855882 |
Based on recent research papers, this book presents a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. It contains an extensive bibliography.
Sobolev Spaces in Mathematics I
Title | Sobolev Spaces in Mathematics I PDF eBook |
Author | Vladimir Maz'ya |
Publisher | Springer Science & Business Media |
Total Pages | 395 |
Release | 2008-12-02 |
Genre | Mathematics |
ISBN | 038785648X |
This volume mark’s the centenary of the birth of the outstanding mathematician of the 20th century, Sergey Sobolev. It includes new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics.
Potential Theory and Degenerate Partial Differential Operators
Title | Potential Theory and Degenerate Partial Differential Operators PDF eBook |
Author | Marco Biroli |
Publisher | Springer Science & Business Media |
Total Pages | 184 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 9401100853 |
Recent years have witnessed an increasingly close relationship growing between potential theory, probability and degenerate partial differential operators. The theory of Dirichlet (Markovian) forms on an abstract finite or infinite-dimensional space is common to all three disciplines. This is a fascinating and important subject, central to many of the contributions to the conference on `Potential Theory and Degenerate Partial Differential Operators', held in Parma, Italy, February 1994.
Fine Regularity of Solutions of Elliptic Partial Differential Equations
Title | Fine Regularity of Solutions of Elliptic Partial Differential Equations PDF eBook |
Author | Jan Malý |
Publisher | American Mathematical Soc. |
Total Pages | 309 |
Release | 1997 |
Genre | Mathematics |
ISBN | 0821803352 |
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.