Two inequalities for the first Robin eigenvalue of the Finsler Laplacian

Abstract

Let Ωbe a bounded connected, open set of \R^n with Lipschitz boundary. Let F be a suitable norm in \R^n and let Δ_F u be the so-colled Finsler Laplacian. In this paper we prove two inequalities for the first eigenvalue of Δ_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 βis a positive constant which goes to zero.

8 pages