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Nonlinear Potential Theory of Degenerate Elliptic Equations
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Product Details
Author:
Juha Heinonen, Tero Kipelainen, Olli Martio
Series:
Dover Books on Mathematics
Format:
Paperback
Pages:
416
Publisher:
Dover Publications (May 16, 2018)
Language:
English
ISBN-13:
9780486824253
ISBN-10:
048682425X
Weight:
16.48oz
Dimensions:
5.5" x 8.5"
Case Pack:
36
File:
Dover-Dover_06012026_P10157433_onix30_Complete-20260601.xml
Folder:
Dover
List Price:
$24.95
As low as:
$23.70
Publisher Identifier:
P-DOVER
Discount Code:
D
Audience:
General/trade
Pub Discount:
65
Imprint:
Dover Publications
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.
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.
