For the fractional Laplacian overdetermined problem with u^{p-1} right-hand side and p in [1,2], every convex C^{1,1} solution domain is a ball.
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Shape derivative approach to fractional overdetermined problems
For the fractional Laplacian overdetermined problem with u^{p-1} right-hand side and p in [1,2], every convex C^{1,1} solution domain is a ball.