Overview
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.
This book title, Nonlinear Potential Theory of Degenerate Elliptic Equations, ISBN: 9780486824253, by Juha Heinonen, Tero Kipelainen, Olli Martio, published by Dover Publications (May 16, 2018) is available in paperback. Our minimum order quantity is 25 copies. All standard bulk book orders ship FREE in the continental USA and delivered in 4-10 business days.
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