{"paper":{"title":"Markov uniqueness of degenerate elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adam Sikora, Derek W. Robinson","submitted_at":"2009-12-22T23:34:03Z","abstract_excerpt":"Let $\\Omega$ be an open subset of $\\Ri^d$ and $H_\\Omega=-\\sum^d_{i,j=1}\\partial_i c_{ij} \\partial_j$ a second-order partial differential operator on $L_2(\\Omega)$ with domain $C_c^\\infty(\\Omega)$ where the coefficients $c_{ij}\\in W^{1,\\infty}(\\Omega)$ are real symmetric and $C=(c_{ij})$ is a strictly positive-definite matrix over $\\Omega$.\n  In particular, $H_\\Omega$ is locally strongly elliptic.\n  We analyze the submarkovian extensions of $H_\\Omega$, i.e. the self-adjoint extensions which generate submarkovian semigroups. Our main result establishes that $H_\\Omega$ is Markov unique, i.e. it h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4536","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"}