Analele Universitatii "Ovidius" Constanta - Seria Matematica Pub Date : 2020-09-22 , DOI: 10.2478/auom-2020-0027
A. E. Nicolescu; S. Vlase

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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