Supersolutions To Degenerate Elliptic Equations On Quasi Open Sets
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Degenerate Elliptic Equations
| Author | : Serge Levendorskii |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 442 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 9401712158 |
This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appropriate weighted Sobolev spaces are given, a priori estimates of solutions are derived, inequalities of the Grding type are proved, and the principal term of the spectral asymptotics for self-adjoint operators is computed. A generalization of the classical Weyl formula is proposed. Some results are new, even for operators of the second order. In addition, an analogue of the Boutet de Monvel calculus is developed and the index is computed. For postgraduate and research mathematicians, physicists and engineers whose work involves the solution of partial differential equations.
Nonlinear Potential Theory of Degenerate Elliptic Equations
| Author | : Juha Heinonen |
| Publisher | : Courier Dover Publications |
| Total Pages | : 417 |
| Release | : 2018-05-16 |
| Genre | : Mathematics |
| ISBN | : 048682425X |
A self-contained treatment appropriate for advanced undergraduate and graduate students, this volume offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Starting with the theory of weighted Sobolev spaces, the text advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The book concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes.
Nonlinear Potential Theory of Degenerate Elliptic Equations
| Author | : Juha Heinonen |
| Publisher | : Courier Dover Publications |
| Total Pages | : 417 |
| 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.
Weighted Sobolev Spaces and Degenerate Elliptic Equations
| Author | : Albo Carlos Cavalheiro |
| Publisher | : Cambridge Scholars Publishing |
| Total Pages | : 333 |
| Release | : 2023-09-29 |
| Genre | : Mathematics |
| ISBN | : 1527551679 |
In various applications, we can meet boundary value problems for elliptic equations whose ellipticity is disturbed in the sense that some degeneration or singularity appears. This bad behavior can be caused by the coefficients of the corresponding differential operator as well as by the solution itself. There are several very concrete problems in various practices which lead to such differential equations, such as glaciology, non-Newtonian fluid mechanics, flows through porous media, differential geometry, celestial mechanics, climatology, and reaction-diffusion problems, among others. This book is based on research by the author on degenerate elliptic equations. This book will be a useful reference source for graduate students and researchers interested in differential equations.
Local And Global Aspects Of Quasilinear Degenerate Elliptic Equations: Quasilinear Elliptic Singular Problems
| Author | : Laurent Veron |
| Publisher | : World Scientific |
| Total Pages | : 474 |
| Release | : 2017-05-05 |
| Genre | : Mathematics |
| ISBN | : 9814730343 |
This book is devoted to the study of elliptic second-order degenerate quasilinear equations, the model of which is the p-Laplacian, with or without dominant lower order reaction term. Emphasis is put on three aspects:
Potential Theory - ICPT 94
| 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.
Fine Regularity of Solutions of Elliptic Partial Differential Equations
| 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.
Elliptic Equations: An Introductory Course
| Author | : Michel Chipot |
| Publisher | : Springer Nature |
| Total Pages | : 393 |
| Release | : |
| Genre | : |
| ISBN | : 3031541235 |
