Abstract
This article investigates how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain in the case when the domains involved are of class . We consider the Laplacian and use results developed previously for the corresponding Lipschitz case. In contrast with the Lipschitz case, however, in the -case we derive an asymptotic formula for the eigenvalues when the domains are of class . Moreover, as an application we consider the case of a -perturbation when the reference domain is of class .
Citation
Johan Thim. "Asymptotics of Hadamard type for eigenvalues of the Neumann problem on $C^1$-domains for elliptic operators." Anal. PDE 8 (7) 1695 - 1706, 2015. https://doi.org/10.2140/apde.2015.8.1695
Information