Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems

Barbara Brandolini, Barbara Brandolini, Francesco Chiacchio, Cristina Trombetti

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ1(Ω) for the p-Laplace operator (p < 1) in a Lipschitz bounded domain Ω in Rn. Our estimate does not require any convexity assumption on Ω and it involves the best isoperimetric constant relative to Ω. In a suitable class of convex planar domains, our bound turns out to be better than the one provided by the Payne-Weinberger inequality.
Original languageEnglish
Pages (from-to)31-45
Number of pages15
JournalPROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS
Volume145
Publication statusPublished - 2015

All Science Journal Classification (ASJC) codes

  • General Mathematics

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