Nonlinear Potential Theory of Degenerate Elliptic Equations (Paperback) (ISBN-13: 9780486824253)

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.

Author: Juha Heinonen, Tero Kipelainen, Olli Martio
ISBN-10: 048682425X
ISBN-13: 9780486824253
Publisher: Dover Publications
Language: English
Published: 05/16/2018
Pages: 416
Format: Paperback
Weight: 1.10lbs
Size: 8.40h x 5.40w x 0.90d