On the lowest eigenvalue of Laplace operators with mixed boundary conditions

Abstract

In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we establish two-sided estimates on the lowest eigenvalues in terms of the inradius and of the boundary conditions.

Cited by in corpus (1)

• Sharp estimates for the first Robin eigenvalue of nonlinear elliptic operators