Nonlinear Potential Theory of Degenerate Elliptic Equations (Oxford Mathematical Monographs) - Hardcover

Heinonen, Juha; Etc.; Kilpelainen, Tero; Martio, Olli

Hardcover

ISBN 10: 0198536690 ISBN 13: 9780198536697

Publisher: Clarendon Press, 1993

Synopsis

This volume provides a detailed introduction to the nonlinear potential theory based on supersolutions to certain degenerate elliptic equations of the p-Laplacian type. Recent research has shown that such classical notions as blayage, polar sets, Perron's method and fine topology have their proper analogues in a nonlinear setting, and a coherent exposition of this natural extension of classical potential theory is presented. Yet fundamental differences to classical potential theory exist, and in many places a new approach is mandatory. Sometimes new, or long forgotten methods emerge that are applicable also to problems in classical potential theory. Quasiregular mappings constitute a natural field of applications and a careful study of the potential theoretic aspects of these mappings is included. The aim of the book is to explore the ground where partial differential equations, harmonic analysis and function theory meet. The quasilinear equations considered in this book involve a degeneracy condition given in terms of a weight function and, therefore, most results appear here for the first time in print. However, the reader interested exlusively in the unweighted theory will find new results, new proofs and a reorganization of the material as compared to the existing literature. No previous knowledge of the subject is required.

About this title

About the Author:

Juha Heinonen (1960 2007) was Professor of Mathematics at the University of Michigan. His principal areas of research interest included quasiconformal mappings, nonlinear potential theory, and analysis on metric spaces. He was the author of over 60 research articles, including several posthumously, and two textbooks. A member of the Finnish Academy of Science and Letters, Heinonen received the Excellence in Research Award from the University of Michigan in 1997 and gave an invited lecture at the International Congress of Mathematicians in Beijing in 2002.

About this edition

• Publisher: Clarendon Press
• Publication date: 1993
• ISBN 10: 0198536690
• ISBN 13: 9780198536697
• Binding: Hardcover
• Number of pages: 368