{"paper":{"title":"Uniqueness of diffusion on domains with rough boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Derek W. Robinson, Juha Lehrb\\\"ack","submitted_at":"2015-04-01T07:34:42Z","abstract_excerpt":"Let $\\Omega$ be a domain in $\\mathbf R^d$ and $h(\\varphi)=\\sum^d_{k,l=1}(\\partial_k\\varphi, c_{kl}\\partial_l\\varphi)$ a quadratic form on $L_2(\\Omega)$ with domain $C_c^\\infty(\\Omega)$ where the $c_{kl}$ are real symmetric $L_\\infty(\\Omega)$-functions with $C(x)=(c_{kl}(x))>0$ for almost all $x\\in \\Omega$. Further assume there are $a, \\delta>0$ such that $a^{-1}d_\\Gamma^{\\delta}\\,I\\le C\\le a\\,d_\\Gamma^{\\delta}\\,I$ for $d_\\Gamma\\le 1$ where $d_\\Gamma$ is the Euclidean distance to the boundary $\\Gamma$ of $\\Omega$.\n  We assume that $\\Gamma$ is Ahlfors $s$-regular and if $s$, the Hausdorff dimens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00127","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"}