ISSN:
0170-4214
Keywords:
Mathematics and Statistics
;
Applied Mathematics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
The 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 ∊ 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)).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/mma.1670120103
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