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Science & Math Books > Mathematics Books
Paperback Nonlinear Potential Theory of Degenerate Elliptic Equations Book
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ISBN: 048682425X

ISBN13: 9780486824253

Nonlinear Potential Theory of Degenerate Elliptic Equations

by , , , et al.
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Book Overview

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.

Related Subjects

Calculus Math Mathematics Science Science & Math Science & Scientists Science & Technology

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