{"paper":{"title":"Heat trace asymptotics and compactness of isospectral potentials for the Dirichlet Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eric Soccorsi (CPT), Laurent Kayser (IECL), Mourad Choulli (IECL), Yavar Kian (CPT)","submitted_at":"2013-12-11T14:06:44Z","abstract_excerpt":"Let $\\Omega$ be a $C^\\infty$-smooth bounded domain of $\\mathbb{R}^n$, $n \\geq 1$, and let the matrix ${\\bf a} \\in C^\\infty (\\overline{\\Omega};\\R^{n^2})$ be symmetric and uniformly elliptic. We consider the $L^2(\\Omega)$-realization $A$ of the operator $-\\mydiv ( {\\bf a} \\nabla \\cdot)$ with Dirichlet boundary conditions. We perturb $A$ by some real valued potential $V \\in C_0^\\infty (\\Omega)$ and note $A_V=A+V$. We compute the asymptotic expansion of $\\mbox{tr}\\left( e^{-t A_V}-e^{-t A}\\right)$ as $t \\downarrow 0$ for any matrix ${\\bf a}$ whose coefficients are homogeneous of degree $0$. In the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3170","kind":"arxiv","version":1},"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"}