{"paper":{"title":"A weighted Sobolev space theory of parabolic stochastic PDEs on non-smooth domains","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kyeong-Hun Kim","submitted_at":"2011-09-22T08:40:09Z","abstract_excerpt":"In this paper we study parabolic stochastic partial differential equations defined on arbitrary bounded domain $\\cO \\subset \\bR^d$ allowing Hardy inequality:\n  $$ \\int_{\\cO}|\\rho^{-1}g|^2\\,dx\\leq C\\int_{\\cO}|g_x|^2 dx, \\quad \\forall g\\in C^{\\infty}_0(\\cO), $$ where $\\rho(x)=\\text{dist}(x,\\partial \\cO)$.\n  Existence and uniqueness results are given in weighted Sobolev spaces $\\frH^{\\gamma}_{p,\\theta}(\\cO,T)$, where $p\\in [2,\\infty)$, $\\gamma\\in \\bR$ is the number of derivatives of solutions and $\\theta$ controls the boundary behavior of solutions. Furthermore several H\\\"older estimates of the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4727","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"}