{"paper":{"title":"On the Lq(Lp)-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.NA"],"primary_cat":"math.PR","authors_text":"Felix Lindner, Kijung Lee, Kyeong-Hun Kim, Petru A. Cioica","submitted_at":"2013-01-07T13:10:23Z","abstract_excerpt":"We investigate the regularity of linear stochastic parabolic equations with zero Dirichlet boundary condition on bounded Lipschitz domains $O \\subset R^d$ with both theoretical and numerical purpose. We use N.V. Krylov's framework of stochastic parabolic weighted Sobolev spaces $\\mathfrak{H}^{\\gamma,q}_{p,\\theta}(O;T)$. The summability parameters p and q in space and time may differ. Existence and uniqueness of solutions in these spaces is established and the H\\\"older regularity in time is analysed. Moreover, we prove a general embedding of weighted Lp(O)-Sobolev spaces into the scale of Besov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1180","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"}