On the estimates of eigenvalues of the boundary value problem with large parameter

Rok, strany: 2015, 101 - 113

We consider the eigenvalue problem $\Delta u+\lambda u=0$ in $\Omega$ with Robin condition $\frac{\partial u}{\partial\nu}+\alpha u=0$ on $\partial\Omega$, where $\Omega\subset R^n$\!, $n \geq 2$ is a bounded domain and $\alpha$ is a real parameter. We obtain the estimates to the difference $\lambda_k^D-\lambda_k(\alpha)$ 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 $k=1,2,\dots$ We also show sharpness of these estimates in the power of $\alpha$.

ISO 690:

Filinovskiy, A. 2015. On the estimates of eigenvalues of the boundary value problem with large parameter. In Tatra Mountains Mathematical Publications, vol. 63, no.2, pp. 101-113. 1210-3195.

APA:

Filinovskiy, A. (2015). On the estimates of eigenvalues of the boundary value problem with large parameter. Tatra Mountains Mathematical Publications, 63(2), 101-113. 1210-3195.