Semi-classical analysis of the Laplace operator with Robin boundary conditions

Rupert L. Frank; Leander Geisinger

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arXiv · 1208.2327

Semi-classical analysis of the Laplace operator with Robin boundary conditions

Rupert L. Frank·Leander Geisinger

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Abstract

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.

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BibTeX RIS

Rupert L. Frank, Leander Geisinger. 2012-08-11. Semi-classical analysis of the Laplace operator with Robin boundary conditions. https://arxiv.org/abs/1208.2327

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