NONLINEAR POTENTIAL THEORY OF DEGENERATE ELLIPTIC EQUATIONS

Book Details:

• Author: Juha Heinonen

• Publisher: Dover

• Binding: Paperback

• Number of Pages: 416

• ISBN-13: 9780486450506

• Languages: English

• Dimensions: 8.4 x 5.1 x 0.9 inches

About The Book:
Nonlinear Potential Theory of Superharmonic Functions by Juha Heinonen is a comprehensive, self-contained treatment designed for advanced undergraduates and graduate students interested in mathematical analysis and potential theory. This text provides a thorough development of the background necessary for a deep understanding of nonlinear potential theory, focusing on superharmonic functions and their properties.

The book begins with an introduction to weighted Sobolev spaces, progressing into the theory of weighted variational capacity. Following chapters explore solutions and supersolutions of equations with an emphasis on refined Sobolev spaces, variational integrals, and harmonic functions.

Chapters 7 through 14 cover the core of nonlinear potential theory, including topics such as:

• Balayage

• Perron’s method, barriers, and resolutivity

• Polar sets and harmonic measure

• Fine topology and harmonic morphisms

• Quasiregular mappings

The text concludes with a section on axiomatic nonlinear potential theory and includes helpful appendices that enhance the reader’s understanding. Suitable for anyone interested in advanced mathematical concepts, this book provides an indispensable resource for those studying or researching in the field of nonlinear potential theory.