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

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  • Barbu, L.
  • Enache, 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.

Suggested Citation

  • Barbu, L. & Enache, C., 2019. "A free boundary problem with multiple boundaries for a general class of anisotropic equations," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:362:y:2019:i:c:42
    DOI: 10.1016/j.amc.2019.06.065
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