{"paper":{"title":"Drift-diffusion equations on domains in $\\mathbb{R}^d$: essential self-adjointness and stochastic completeness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Gheorghe Nenciu, Irina Nenciu","submitted_at":"2016-09-25T01:33:10Z","abstract_excerpt":"We consider the problem of quantum and stochastic confinement for drift-diffusion equations on domains $ \\Omega \\subset \\mathbb R^d$. We obtain various sufficient conditions on the behavior of the coefficients near the boundary of $\\Omega$ which ensure the essential self-adjointness or stochastic completeness of the symmetric form of the drift-diffusion operator, $-\\frac{1}{\\rho_\\infty}\\,\\nabla\\cdot \\rho_\\infty\\mathbb D\\nabla$. The proofs are based on the method developed in [29] for quantum confinement on bounded domains in $\\mathbb R^d$. In particular for stochastic confinement we combine th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07689","kind":"arxiv","version":2},"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"}