Some decomposition theorems and their application to non‐linear potential theory and Hodge theory
作者:
Rainer Picard,
期刊:
Mathematical Methods in the Applied Sciences
(WILEY Available online 1990)
卷期:
Volume 12,
issue 1
页码: 35-52
ISSN:0170-4214
年代: 1990
DOI:10.1002/mma.1670120103
出版商: John Wiley&Sons, Ltd
数据来源: WILEY
摘要:
AbstractThe paper considers Dirichlet (or Neumann type) boundary value problems of generalized potential theory\documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm d}\alpha = f,\;\delta \varepsilon \left(\alpha \right) = g\,{\rm in}\,M, $$\end{document}\documentclass{article}\pagestyle{empty}\begin{document}$$ \alpha = 0\,{\rm on}\,\partial M $$\end{document}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 Ma
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