{"paper":{"title":"H\\\"older regularity for a non-linear parabolic equation driven by space-time white noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Felix Otto, Hendrik Weber","submitted_at":"2015-05-04T20:58:25Z","abstract_excerpt":"We consider the non-linear equation $T^{-1} u+\\partial_tu-\\partial_x^2\\pi(u)=\\xi$ driven by space-time white noise $\\xi$, which is uniformly parabolic because we assume that $\\pi'$ is bounded away from zero and infinity. Under the further assumption of Lipschitz continuity of $\\pi'$ we show that the stationary solution is - as for the linear case - almost surely H\\\"older continuous with exponent $\\alpha$ for any $\\alpha<\\frac{1}{2}$ w. r. t. the parabolic metric. More precisely, we show that the corresponding local H\\\"older norm has stretched exponential moments.\n  On the stochastic side, we u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00809","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"}