Preprint 52/2006

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

Hayk Mikayelyan and Henrik Shahgholian

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Submission date: 18. May. 2006 (revised version: August 2006)
Pages: 17
paper submitted
Keywords and phrases: free boundary problems, perimeter, convexity
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Abstract:
We prove that if the given compact set K is convex then a minimizer of the functional
displaymath12
over the set formula14 has a convex support, and as a result all its level sets are convex as well. We derive the free boundary condition for the minimizers and prove that the free boundary is analytic and the minimizer is unique.

27.07.2013, 01:41