Convexity of the free boundary for an exterior free boundary problem involving the perimeter

Details Convexity of the free boundary for an exterior free boundary problem involving the perimeter Convexity of the free boundary for an exterior free boundary problem involving the perimeter

2010-10-14

arxiv.org/abs/1010.2960v1

Mathematics

Analysis of PDEs

Scientific paper

We prove that if the given compact set $K$ is convex then a minimizer of the functional $$ I(v)=\int_{B_R} |\nabla v|^p dx+\text{Per}(\{v>0\}),\,1

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