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On some overdetermined free boundary problems. (English) Zbl 1333.35349

Summary: This paper deals with some free boundary problems for the Laplacian operator. We first give sufficient conditions of existence of free boundaries. Then combining the maximum principle to the monotonicity of the mean curvature, we will prove a symmetry result in the case where the source term is constant. All the results obtained here can be extended to more general divergence operators.

MSC:

35R35 Free boundary problems for PDEs
35N05 Overdetermined systems of PDEs with constant coefficients
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