Given an open set $\Omega$, we consider the problem of providing sharp lower bounds for $\lambda_2(\Omega)$, i.e. its second Dirichlet eigenvalue of the $p-$Laplace operator. After presenting the nonlinear analogue of the {\it Hong-Krahn-Szego inequality}, asserting that the disjoint unions of two equal balls minimize $\lambda_2$ among open sets of given measure, we improve this spectral inequality by means of a quantitative stability estimate. The extremal cases $p=1$ and $p=\infty$ are considered as well.
On the Hong-Krahn-Szego inequality for the $p-$Laplace operator
BRASCO, Lorenzo;
2013
Abstract
Given an open set $\Omega$, we consider the problem of providing sharp lower bounds for $\lambda_2(\Omega)$, i.e. its second Dirichlet eigenvalue of the $p-$Laplace operator. After presenting the nonlinear analogue of the {\it Hong-Krahn-Szego inequality}, asserting that the disjoint unions of two equal balls minimize $\lambda_2$ among open sets of given measure, we improve this spectral inequality by means of a quantitative stability estimate. The extremal cases $p=1$ and $p=\infty$ are considered as well.File in questo prodotto:
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