Author: Peter LindqvistPublisher:
ISBN:
Category :
Languages : en
Pages : 50
Book Description
Regularity and Polar Sets for Supersolutions of Certain Degenerate Elliptic Equations
Author: Peter LindqvistRegularity and Polar Sets for Supersolutions of Certian Degenerate Elliptic Equations
Author: Peter LindqvistPolar Sets for Supersolutions of Degenerate Elliptic Equations
Author: Juha HeinonenNonlinear Potential Theory of Degenerate Elliptic Equations
Author: Juha HeinonenPublisher: Courier Dover Publications
ISBN: 0486830462
Category : Mathematics
Languages : en
Pages : 417
Book Description
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.
Singularities of Solutions of Second-Order Quasilinear Equations
Author: Laurent VeronPublisher: CRC Press
ISBN: 9780582035393
Category : Mathematics
Languages : en
Pages : 396
Book Description
This text examines the singularity problem for solutions of elliptic and parabolic quasilinear equations of second order.
Fine Regularity of Solutions of Elliptic Partial Differential Equations
Author: Jan MalýPublisher: American Mathematical Soc.
ISBN: 0821803352
Category : Mathematics
Languages : en
Pages : 309
Book Description
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.
Nonlinear Potential Theory of Degenerate Elliptic Equations
Author: Juha HeinonenPublisher: Courier Dover Publications
ISBN: 048682425X
Category : Mathematics
Languages : en
Pages : 417
Book Description
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.
Potential Theory
Author: Josef KralPublisher: Springer Science & Business Media
ISBN: 1461309816
Category : Mathematics
Languages : en
Pages : 352
Book Description
Within the tradition of meetings devoted to potential theory, a conference on potential theory took place in Prague on 19-24, July 1987. The Conference was organized by the Faculty of Mathematics and Physics, Charles University, with the collaboration of the Institute of Mathematics, Czechoslovak Academy of Sciences, the Department of Mathematics, Czech University of Technology, the Union of Czechoslovak Mathematicians and Physicists, the Czechoslovak Scientific and Technical Society, and supported by IMU. During the Conference, 69 scientific communications from different branches of potential theory were presented; the majority of them are in cluded in the present volume. (Papers based on survey lectures delivered at the Conference, its program as well as a collection of problems from potential theory will appear in a special volume of the Lecture Notes Series published by Springer-Verlag). Topics of these communications truly reflect the vast scope of contemporary potential theory. Some contributions deal with applications in physics and engineering, other concern potential theoretic aspects of function theory and complex analysis. Numerous papers are devoted to the theory of partial differential equations. Included are also many articles on axiomatic and abstract potential theory with its relations to probability theory. The present volume may thus be of intrest to mathematicians speciali zing in the above-mentioned fields and also to everybody interested in the present state of potential theory as a whole.
The Local Regularity of Solutions of Degenerate Elliptic Equations
Author: Eugene B. FabesDegenerate Elliptic Equations
Author: Serge LevendorskiiPublisher: Springer Science & Business Media
ISBN: 9401712158
Category : Mathematics
Languages : en
Pages : 442
Book Description
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.