On a free boundary problem for a class of anisotropic equations |
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| Authors: | Luminita Barbu Cristian Enache |
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| Institution: | 1. Department of Mathematics, Ovidius University of Constanta, Constanta, Romania;2. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab Emirates |
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| Abstract: | This paper deals with a certain condenser capacity in an anisotropic environment. More precisely, we are going to investigate a free boundary problem for a class of anisotropic equations on a ring domain  N≥2. Our aim is to show that if the problem admits a solution in a suitable weak sense, then the underlying domain Ω is a Wulff‐shaped ring. The proof makes use of a maximum principle for an appropriate P‐function, in the sense of L. E. Payne, a Rellich type identity and some geometric arguments involving the anisotropic mean curvature of the free boundary. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | anisotropic equations maximum principles overdetermined problems Wulff shapes |
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N≥2. Our aim is to show that if the problem admits a solution in a suitable weak sense, then the underlying domain Ω is a Wulff‐shaped ring. The proof makes use of a maximum principle for an appropriate P‐function, in the sense of L. E. Payne, a Rellich type identity and some geometric arguments involving the anisotropic mean curvature of the free boundary. Copyright © 2016 John Wiley & Sons, Ltd.