Sharp Estimates for Eigenfunctions of a Neumann Problem
Barbara Brandolini, Ferdınando Chıacchıo, Cristina Trombetti · Communications in Partial Differential Equations · 2009
In this paper we provide some bounds for eigenfunctions of the Laplacian with homogeneous Neumann boundary conditions in a bounded domain Ω of ℝ n . To this aim we use the so-called symmetrization techniques and the obtained estimates are asymptotically sharp, at least in the bidimensional case, when the isoperimetric constant relative to Ω goes to 0.