On a free boundary value problem for the anisotropic N-Laplace operator on an N−dimensional ring domain

A. E. Nicolescu 1  and S. Vlase 2
  • 1 Doctoral School of Mathematics, Ovidius University of Constanta, Bdul Mamaia 124, 900527, Constanta, Romania
  • 2 Department of Mechanical Engineering, Transilvania University of Brasov, 500118, Brasov, Romania

Abstract

In this paper we are going to investigate a free boundary value problem for the anisotropic N-Laplace operator on a ring domain Ω:=Ω0\Ω¯1𝕉N, 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 and some geometric arguments involving the anisotropic mean curvature of the free boundary.

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