Optimal Szegö-Weinberger type inequalities
Optimal Szegö-Weinberger type inequalities
Denote with $\mu _{1}(\Omega ;e^{h( |x|) })$ the first nontrivialeigenvalue of the Neumann problem\begin{eqnarray}&-div( e^{h( |x|) }\nabla u) =\mu e^{h(|x|) }u \quad in \ \Omega \\&\frac{\partial u}{\partial \nu }=0 \quad on \ \partial \Omega,\end{eqnarray}where $\Omega $ is a bounded and Lipschitz domain in $\mathbb{R}^{N}$. Undersuitable assumption on $h$ we prove …