Publisher's 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.
