Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems

B. Brandolini; F. Chiacchio; C. Trombetti

Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems

Analysis of PDEs 2013-02-08 v1

Authors: B. Brandolini , F. Chiacchio , C. Trombetti

Abstract

In this paper we prove a sharp lower bound for the first nontrivial Neumann eigenvalue $\mu_1(\Omega)$ for the $p$ -Laplace operator in a Lipschitz, bounded domain $\Omega$ in $\R^n$ . Our estimate does not require any convexity assumption on $\Omega$ and it involves the best isoperimetric constant relative to $\Omega$ .

Keywords

laplacian eigenvalues bounded domains laplacian eigenfunctions

Cite

@article{arxiv.1302.1795,
  title  = {Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems},
  author = {B. Brandolini and F. Chiacchio and C. Trombetti},
  journal= {arXiv preprint arXiv:1302.1795},
  year   = {2013}
}

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