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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0912.4536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-12-22T23:34:03Z","cross_cats_sorted":[],"title_canon_sha256":"a97a866ba76baa876ad0b1f20ebf65a7dd3d6369907d59d5d3975b70e8a88944","abstract_canon_sha256":"048e0fe1049c0539c46253c8045cf77fda788cf15c9a23dcb5a5ae65cbfb79ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:33.126851Z","signature_b64":"R+KD6bU/uG6Jc7qKIkntwzdJK0qYC98hKKqlpBpdKnTIMJkY9NUNFu0uHnKaQEfpCobISjEswqTRllf5sUVZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f9b4d945f9dcca5f73d20934ada2e9b75df1f43b2c5fc28e553fd1a3df0c2b5","last_reissued_at":"2026-05-18T03:03:33.126045Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:33.126045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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