Daners, Daniel; Kennedy, James B. On the asymptotic behaviour of the eigenvalues of a Robin problem. (English) Zbl 1240.35370 Differ. Integral Equ. 23, No. 7-8, 659-669 (2010). The authors prove that every eigenvalue of a Robin problem \(-\Delta u=\lambda u\) in \(\Omega \), \(\frac {\partial u}{\partial \nu }=\alpha u\) on \(\partial \Omega ,\) where \(\alpha \) is a positive boundary parameter and \(\Omega \subset \mathbb {R}^{n}\) is a bounded domain of class \(C^1,\) behaves asymptotically like \(-\alpha ^2\) as \(\alpha \rightarrow \infty \). This generalizes an existing result for the first eigenvalue. Reviewer: Jana Stará (Praha) Cited in 26 Documents MSC: 35P15 Estimates of eigenvalues in context of PDEs 35B40 Asymptotic behavior of solutions to PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation Keywords:eigenvalue; Robin problem; Laplacian PDFBibTeX XMLCite \textit{D. Daners} and \textit{J. B. Kennedy}, Differ. Integral Equ. 23, No. 7--8, 659--669 (2010; Zbl 1240.35370) Full Text: arXiv