{"paper":{"title":"Sharp norm estimates of layer potentials and operators at high frequency","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jeffrey Galkowski, Melissa Tacy, Xiaolong Han","submitted_at":"2014-03-26T06:49:25Z","abstract_excerpt":"In this paper, we investigate single and double layer potentials mapping boundary data to interior functions of a domain at high frequency $\\lambda^2\\to\\infty$. For single layer potentials, we find that the $L^{2}(\\partial\\Omega)\\to{}L^{2}(\\Omega)$ norms decay in $\\lambda$. The rate of decay depends on the curvature of $\\partial\\Omega$: The norm is $\\lambda^{-3/4}$ in general domains and $\\lambda^{-5/6}$ if the boundary $\\partial\\Omega$ is curved. The double layer potential, however, displays uniform $L^{2}(\\partial\\Omega)\\to{}L^{2}(\\Omega)$ bounds independent of curvature. By various examples"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6576","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}