{"paper":{"title":"A note on space-time Holder regularity of mild solutions to stochastic Cauchy problems in Lp-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Rafael Serrano","submitted_at":"2014-05-01T01:29:14Z","abstract_excerpt":"This paper revisits the H\\\"{o}lder regularity of mild solutions of parabolic stochastic Cauchy problems in Lebesgue spaces $L^p(\\mathcal{O}),$ with $p\\geq 2$ and $\\mathcal{O}\\subset\\mathbb{R}^d$ a bounded domain. We find conditions on $p, \\beta$ and $\\gamma$ under which the mild solution has almost surely trajectories in $\\mathcal{C}^\\beta([0,T];\\mathcal{C}^\\gamma(\\bar{\\mathcal{O}})).$ These conditions do not depend on the Cameron-Martin Hilbert space associated with the driving cylindrical noise. The main tool of this study is a regularity result for stochastic convolutions in M-type 2 Banach"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0075","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"}