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

revised version: August 2006
Hayk Mikayelyan, and Henrik Shahgholian
(Please use for correspondence this email).

Submission date: 18. May. 2006
Pages: 17
paper submitted
Keywords and phrases: free boundary problems, perimeter, convexity
Download preprint: PDF (219 kB)

Abstract:
We prove that if the given compact set K is convex then a minimizer of the functional

over the set 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.