Degenerate elliptic equations with measure data and nonlinear potentials PDF Download

Author: Tero Kilpeläinen
Publisher:
ISBN:
Category :
Languages : en
Pages : 22

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Author: Juha Heinonen
Publisher: Courier Dover Publications
ISBN: 9780486450506
Category : Calculus of variations
Languages : en
Pages : 0

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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. Starting with the theory of weighted Sobolev spaces, this treatment 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 text concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes.

Author: Juha Heinonen
Publisher: Courier Dover Publications
ISBN: 0486830462
Category : Mathematics
Languages : en
Pages : 417

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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.

Author: Serge Levendorskii
Publisher: Springer Science & Business Media
ISBN: 9401712158
Category : Mathematics
Languages : en
Pages : 442

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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.

Author: Emmanuele DiBenedetto
Publisher: Springer Science & Business Media
ISBN: 1461208955
Category : Mathematics
Languages : en
Pages : 402

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Evolved from the author's lectures at the University of Bonn's Institut für angewandte Mathematik, this book reviews recent progress toward understanding of the local structure of solutions of degenerate and singular parabolic partial differential equations.

Author: Laurent Veron
Publisher: World Scientific
ISBN: 9814730343
Category : Mathematics
Languages : en
Pages : 474

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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:

Author: A. V. Ivanov
Publisher: American Mathematical Soc.
ISBN: 9780821830802
Category : Mathematics
Languages : en
Pages : 306

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Author: Josef Kral
Publisher: Walter de Gruyter
ISBN: 3110818574
Category : Mathematics
Languages : en
Pages : 513

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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.

Author: Albo Carlos Cavalheiro
Publisher: Cambridge Scholars Publishing
ISBN: 1527551679
Category : Mathematics
Languages : en
Pages : 333

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Book Description
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.

Author: Quoc-Hung Nguyen
Publisher: American Mathematical Society
ISBN: 1470467224
Category : Mathematics
Languages : en
Pages : 136

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