We consider the eigenvalue problem $\Delta u + \Lambda u = 0$ in $\Omega$ with Robin condition $\frac {\delta u}{\delta \nu} + \alpha u = 0$ on $\delta\Omega$, where $\Omega \subset \R^n, n\geq 2$ is a bounded domain with $\delta\Omega\in C^2, \alpha$ is a real parameter. We obtain the estimates to the difference \lambda^D_k - \lamda_k(\alpha) between $k$-th eigenvalue of the Laplace operator in \Omega with Dirichlet condition and the corresponding Robin eigenvalue for large positive values of \alpha for all $k= 1,2,\ldots$ We also show sharpness of these estimates in the pover of $\alpha$.
@article{341,
title = {On the estimates of eigenvalues of the boundary value problem with large parameter},
journal = {Tatra Mountains Mathematical Publications},
volume = {62},
year = {2015},
doi = {10.2478/tatra.v63i0.341},
language = {EN},
url = {http://dml.mathdoc.fr/item/341}
}
Filinovskiy, Alexey Vladislavovich. On the estimates of eigenvalues of the boundary value problem with large parameter. Tatra Mountains Mathematical Publications, Tome 62 (2015) . doi : 10.2478/tatra.v63i0.341. http://gdmltest.u-ga.fr/item/341/