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Nonlinear Potential Theory of Degenerate Elliptic Equations (Dover Books on Mathematics) - Softcover

Book 133 of 302: Dover Books on Mathematics

Walecka, John Dirk; Heinonen, Juha

 
9780486824253: Nonlinear Potential Theory of Degenerate Elliptic Equations (Dover Books on Mathematics)
Softcover
ISBN 10: 048682425X ISBN 13: 9780486824253
Publisher: Dover Publications Inc, 2018

Synopsis

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.

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Publisher
Dover Publications Inc
Publication date
2018
Language
English
ISBN 10 
048682425X
ISBN 13 
9780486824253
Binding
Paperback
Number of pages
416

Other Popular Editions of the Same Title

9780486450506: Nonlinear Potential Theory of Degenerate Elliptic Equations (Dover Books on Mathematics)

Featured Edition

ISBN 10:  0486450503 ISBN 13:  9780486450506
Publisher: Dover Publications Inc., 2006
Softcover