## 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 $$\alpha\to\infty$$. This generalises an existing result for the first eigenvalue.

Keywords: Laplacian, Robin boundary conditions, eigenvalue asymptotics.

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

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 Friday, December 11, 2009