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Optimal Szegö-Weinberger type inequalities
2016
Communications on Pure and Applied Analysis
Denote with µ 1 (Ω; e h(|x|) ) the first nontrivial eigenvalue of the Neumann problem where Ω is a bounded and Lipschitz domain in R N . Under suitable assumption on h we prove that the ball centered at the origin is the unique set maximizing µ 1 (Ω; e h(|x|) ) among all Lipschitz bounded domains Ω of R N of prescribed e h(|x|) dx-measure and symmetric about the origin. Moreover, an example in the model case h (|x|) = |x| 2 , shows that, in general, the assumption on the symmetry of the domain
doi:10.3934/cpaa.2016.15.367
fatcat:z6jcq2watzakfb5dx7ozsh4lxi