On Serrin’s symmetry result in nonsmooth domains and its applications
نویسنده
چکیده
The goal of this paper is to show that Serrin’s result on overdetermined problems holds true for symmetric non-smooth domains. Specifically, we show that if a non-smooth domain D satisfies appropriate symmetry and convexity assumptions, and there exists a positive solution to a general overdetermined problem on D, then D must be a ball. As an application, we improve results on symmetry of non-negative solutions of Dirichlet problems.
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