Nonlinear Potential Theory of Degenerate Elliptic Equations (Dover Books on Mathematics) by Juha Heinonen (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Great Book, it provides a really good introduction to the theory of capacities.

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⭐The three authors are experts, their presentation is unique and to the point – definitely highly recommendable. Another Plus: The more than fair Dover price!

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