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

Heinonen, Juha; Kilpeläinen, Tero; Martio, Olli

Hardcover

ISBN 10: 0198536690 ISBN 13: 9780198536697

Publisher: Oxford University Press, 1993

Synopsis

This book provides a detailed introduction to nonlinear potential theory based on supersolutions to certain degenerate elliptic equations of the p-Laplacian type. Recent research has shown that classical notions such as blayage, polar sets, Perron's method, and fine topology have their proper analogues in a nonlinear setting, and this book presents a coherent exposition of this natural extension of classical potential theory. 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 to problems in classical potential theory. Quasiregular mappings constitute a natural field of applications, and a careful study of the potential theoretical aspects of these mappings is included. The principle 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. The reader interested exclusively in the unweighted theory will find new results, new proofs, and a reorganization of the material as compared to the existing literature. The book is intended for researchers and graduate students in potential theory, variational calculus, partial differential equations, and quasiconformal mappings.

About this title

About the Author

Juha Heinonen, Assistant Professor of Mathematics, University of Michigan. Tero Kilpelainen, Docent of Mathematics, University of Jyvaskyla. Olli Martio, Professor, Department of Mathematics, University of Jyvaskyla.

Edition details

• Publisher: Oxford University Press
• Publication date: 1993
• Language: English
• ISBN 10: 0198536690
• ISBN 13: 9780198536697
• Binding: Hardcover
• Number of pages: 368