We prove that the only domain such that there exists a solution to the following problem in , on , and , for a given constant , is the unit ball , if we assume that lies in an appropriate class of Lipschitz domains.
B. Canuto, A local symmetry result for linear elliptic problems with solutions changing sign. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 4, pp. 551–564
DOI 10.1016/J.ANIHPC.2011.03.005