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Some decomposition theorems and their application to non-linear potential theory and Hodge theory

✍ Scribed by Rainer Picard

Publisher
John Wiley and Sons
Year
1990
Tongue
English
Weight
813 KB
Volume
12
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

The paper considers Dirichlet (or Neumann type) boundary value problems of generalized potential theory

on Lipschitz manifolds with boundary. Here ϵ denotes a permissible non‐linearity. The existence theory is developed in the framework of monotone operators. The approach covers a variety of applications including fluid dynamics and electro‐ and magneto‐statics. Only fairly weak regularity assumptions are required (e.g. Lipschitz boundary, L~∞~‐coefficients). As a by‐product we obtain a non‐linear Hodge theorem generalizing a result by L. M. Sibner and R. J. Sibner (‘A non‐linear Hodge‐DeRham theorem’, Acta Math., 125, 57–73 (1970)).

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