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Nonlinear Potential Theory of Degenerate Elliptic Equations

Nonlinear Potential Theory of Degenerate Elliptic Equations

By: Olli Martio, Juha Heinonen, Tero Kilpeläinen

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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.

Slightly corrected republication of the edition published by Oxford University Press, New York, 1993.
AvailabilityUsually ships in 24 to 48 hours
ISBN 100486450503
ISBN 139780486450506
Author/EditorOlli Martio, Juha Heinonen, Tero Kilpeläinen
Page Count416
Dimensions5 3/8 x 8 1/2

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