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On a free boundary problem in electrostatics

✍ Scribed by G. A. Philippin

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

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✦ Synopsis

Abstract

Let Ξ©~i~ βŠ‚ ℝ^N^, i = 0, 1, be two bounded separately star‐shaped domains such that \documentclass{article}\pagestyle{empty}\begin{document}$ \Omega _0 \supset \bar \Omega _1 $\end{document}. We consider the electrostatic potential u defined in \documentclass{article}\pagestyle{empty}\begin{document}$ \Omega : = \Omega _0 \backslash \bar \Omega _1 $\end{document}:

The geometry of the two boundary components Ξ“~0~ and Ξ“~1~ is not given, but instead the electrostatic potential u is supposed to satisfy the further boundary conditions
magnified image
Using a best possible maximum principle, we show that this free boundary problem has a unique solution which is radially symmetric.

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