Nonlinear Potential Theory of Degenerate Elliptic Equations - Brossura

Heinonen, Juha; Kilpelainen, Tero; Martio, Olli

Brossura

ISBN 10: 0486450503 ISBN 13: 9780486450506

Casa editrice: Dover Pubns, 2006

Riassunto

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.

Su questo libro

Product Description

This text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Topics include the theory of weighted variational capacity; solutions and supersolutions of equation; balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; more. 1993 edition.

Dettagli dell?edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2006
• ISBN 10: 0486450503
• ISBN 13: 9780486450506
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 404