Best constants in Poincaré inequalities for convex domains

2011/10/13 by L. Esposito, C. Nitsch, Esposito, L. +3
Mathematics · #26D10 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:26D10 #msc:35J92

paper · pdf · doi:10.48550/arxiv.1110.2960

arxiv created 2011/10/13 · arxiv updated 2011/10/14

Abstract

We prove a Payne-Weinberger type inequality for the p-Laplacian Neumann eigenvalues (p≥ 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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