Nonlinear Potential Theory of Degenerate Elliptic Equations
Nonlinear Potential Theory of Degenerate Elliptic Equations

Author: Juha Heinonen

Publisher: Courier Dover Publications

Published: 2018-05-16

Total Pages: 417

ISBN-13: 048682425X

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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
Nonlinear Potential Theory of Degenerate Elliptic Equations

Author: Juha Heinonen

Publisher: Courier Dover Publications

Published: 2018-05-16

Total Pages: 417

ISBN-13: 0486830462

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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.

Nonlinear Potential Theory and Weighted Sobolev Spaces
Nonlinear Potential Theory and Weighted Sobolev Spaces

Author: Bengt O. Turesson

Publisher: Springer

Published: 2007-05-06

Total Pages: 188

ISBN-13: 3540451684

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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
Potential Theory - ICPT 94

Author: Josef Kral

Publisher: Walter de Gruyter

Published: 2011-10-13

Total Pages: 513

ISBN-13: 3110818574

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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.

Nonlinear Evolution Equations and Potential Theory
Nonlinear Evolution Equations and Potential Theory

Author: J. Kral

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 138

ISBN-13: 1461344255

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Preface.- Gottfried Anger: Direct and inverse problems in potential theory.- Viorel Barbu: Regularity results for sane differential equations associated with maximal monotone operators in Hilbert spaces.- Haim Brezis: Classes d'interpolation associées à un opérateur monotone et applications.- Siegfried Dnümmel: On inverse problems for k-dimensional potentials.- Jozef Ka?ur: Application of Rothe's method to nonlinear parabolic boundary value problems.- Josef Král: Potentials and removability of singularities.- Vladimir Lovicar: Theorem of Fréchet and asymptotically almost periodid solutions of.

Moduli in Modern Mapping Theory
Moduli in Modern Mapping Theory

Author: Olli Martio

Publisher: Springer Science & Business Media

Published: 2008-11-09

Total Pages: 368

ISBN-13: 0387855882

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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
Sobolev Spaces in Mathematics I

Author: Vladimir Maz'ya

Publisher: Springer Science & Business Media

Published: 2008-12-02

Total Pages: 395

ISBN-13: 038785648X

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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.