Two inequalities for the first Robin eigenvalue of the Finsler Laplacian
Abstract
Let be a bounded connected, open set of n with Lipschitz boundary. Let F be a suitable norm in n and let F u be the so-colled Finsler Laplacian. In this paper we prove two inequalities for the first eigenvalue of F with Robin boundary conditions involving a positive function β. As a consequence of our result we obtain the asymptotic behavior of this eigenvalue when β is a positive constant which goes to zero.
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