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 constant 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.

Author information

Contact details are reproduced from the original publication and may be historical.

Luca Esposito

Dip. di Matematica e Informatica, Università di Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

luesposi@unisa.it

Carlo Nitsch

Dip. di Matematica e Applicazioni, Università di Napoli, Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, Italy

c.nitsch@unina.it

Cristina Trombetti

Dip. di Matematica e Applicazioni, Università di Napoli, Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, Italy

cristina@unina.it

Keywords

  • Poincaré inequality
  • p-Laplacian eigenvalues
  • Neumann boundary conditions

Mathematics Subject Classification

35B05, 47J05, 26D15

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Suggested citation

L. Esposito, C. Nitsch, C. Trombetti. “Best Constants in Poincaré Inequalities for Convex Domains.” Journal of Convex Analysis 20 (2013), No. 1, 253–264. https://doi.org/10.68381/jca20016

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Published by Heldermann Verlag, 2013. Rights now held by Banach Press LLC.