{"paper":{"title":"The fractional nonlocal Ornstein--Uhlenbeck equation, Gaussian symmetrization and regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA","math.PR"],"primary_cat":"math.AP","authors_text":"B. Volzone, F. Feo, P. R. Stinga","submitted_at":"2017-01-04T16:41:13Z","abstract_excerpt":"For $0<s<1$, we consider the Dirichlet problem for the fractional nonlocal Ornstein--Uhlenbeck equation $$\\begin{cases} (-\\Delta+x\\cdot\\nabla)^su=f&\\hbox{in}~\\Omega\\\\ u=0&\\hbox{on}~\\partial\\Omega, \\end{cases}$$ where $\\Omega$ is a possibly unbounded open subset of $\\mathbb{R}^n$, $n\\geq2$. The appropriate functional settings for this nonlocal equation and its corresponding extension problem are developed. We apply Gaussian symmetrization techniques to derive a concentration comparison estimate for solutions. As consequences, novel $L^p$ and $L^p(\\log L)^\\alpha$ regularity estimates in terms of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01068","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"}