Concentration of eigenfunctions near a concave boundary
Analysis of PDEs
2011-11-01 v5
Abstract
This paper concerns the concentration of Dirichlet eigenfunctions of the Laplacian on a compact two-dimensional Riemannian manifold with strictly geodesically concave boundary. We link three inequalities which bound the concentration in different ways. We also prove one of these inequalities, which bounds the L^p norms of the restrictions of eigenfunctions to broken geodesics.
Cite
@article{arxiv.1007.0231,
title = {Concentration of eigenfunctions near a concave boundary},
author = {Sinan Ariturk},
journal= {arXiv preprint arXiv:1007.0231},
year = {2011}
}
Comments
32 pages. Made more corrections.arXiv admin note: substantial text overlap with arXiv:1007.0230