A free boundary problem with multiple boundaries for a general class of anisotropic equations

L. Barbu and C. Enache

Applied Mathematics and Computation, 2019, vol. 362, issue C, -

Abstract: In this paper we are going to investigate a free boundary problem for a class of anisotropic equations on a multiply-connected domain Ω⊂RN,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. This result represents the anisotropic extension of a result obtained by Payne and Philippin (1991) [13]. For the proof, we make use of a maximum principle for an appropriate P-function, a Rellich type identity, an anisotropic form of Minkowski inequality for convex sets and some geometric arguments involving the anisotropic mean curvatures of the free boundaries.

Keywords: Anisotropic equations; Maximum principles; Overdetermined problems; Wulff shapes (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:362:y:2019:i:c:42

DOI: 10.1016/j.amc.2019.06.065

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