%0 Journal Article
%T Semi-classical analysis of the Laplace operator with Robin boundary conditions
%A Rupert L. Frank
%A Leander Geisinger
%J Bulletin of Mathematical Sciences
%@ 1664-3615
%D 2012
%I Springer
%R 10.1007/s13373-012-0028-5
%X We prove a two-term asymptotic expansion of eigenvalue sums of the Laplacian on a bounded domain with Neumann, or more generally, Robin boundary conditions. We formulate and prove the asymptotics in terms of semi-classical analysis. In this reformulation it is natural to allow the function describing the boundary conditions to depend on the semi-classical parameter and we identify and analyze three different regimes for this dependence.
%U http://link.springer.com/article/10.1007/s13373-012-0028-5