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

Walecka, John Dirk; Heinonen, Juha

Softcover

ISBN 10: 048682425X ISBN 13: 9780486824253

Verlag: Dover Publications Inc, 2018

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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.
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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Über diese Auflage

• Verlag: Dover Publications Inc
• Erscheinungsdatum: 2018
• ISBN 10: 048682425X
• ISBN 13: 9780486824253
• Einband: Tapa blanda
• Anzahl der Seiten: 416