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arXiv · 1110.2960

Best constants in Poincaré inequalities for convex domains

L. Esposito·C. Nitsch·C. Trombetti
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Abstract

We prove a Payne-Weinberger type inequality for the $p$-Laplacian Neumann eigenvalues ($p\ge 2$). The inequality provides the sharp upper bound on convex domains, in terms of the diameter alone, of the best constants in Poincaré inequality. The key point is the implementation of a refinement of the classical Pólya-Szegö inequality for the symmetric decreasing rearrangement which yields an optimal weighted Wirtinger inequality.

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L. Esposito, C. Nitsch, C. Trombetti. 2011-10-13. Best constants in Poincaré inequalities for convex domains. https://arxiv.org/abs/1110.2960

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