{"paper":{"title":"Gaussian bounds, strong ellipticity and uniqueness criteria","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Derek W. Robinson","submitted_at":"2014-01-02T03:05:05Z","abstract_excerpt":"Let $h$ be a quadratic form with domain $W_0^{1,2}(\\Ri^d)$ given by \\[ h(\\varphi)=\\sum^d_{i,j=1}(\\partial_i\\varphi,c_{ij}\\,\\partial_j\\varphi) \\] where $c_{ij}=c_{ji}$ are real-valued, locally bounded, measurable functions and\n  $C=(c_{ij})\\geq 0 $.\n  If $C$ is strongly elliptic, i.e.\\ if there exist $\\lambda, \\mu>0$ such that $\\lambda\\,I\\geq C\\geq \\mu \\,I>0$, then $h$ is closable, the closure determines a positive self-adjoint operator $H$ on $L_2(\\Ri^d)$ which generates a submarkovian semigroup $S$ with a positive distributional kernel~$K$ and the kernel satisfies Gaussian upper and lower bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0360","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"}