On the asymptotic behaviour of the eigenvalues of a Robin problem

Daniel Daners and James B. Kennedy

Abstract

We prove that every eigenvalue of a Robin problem with boundary parameter $\alpha$ on a sufficiently smooth domain behaves asymptotically like $-{\alpha }^2$ as $\alpha \to \mathrm{\infty }$. This generalises an existing result for the first eigenvalue.

Keywords: Laplacian, Robin boundary conditions, eigenvalue asymptotics.

AMS Subject Classification: Primary 35P15; secondary (35B40, 35J05).