{"paper":{"title":"Conical stochastic maximal $L^p$-regularity for $1 \\leq p \\lt \\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.PR"],"primary_cat":"math.CA","authors_text":"Jan van Neerven (TWA), Pascal Auscher (LM-Orsay), Pierre Portal (MSI)","submitted_at":"2011-12-14T13:10:51Z","abstract_excerpt":"Let $A = -{\\rm div} \\,a(\\cdot) \\nabla$ be a second order divergence form elliptic operator on $\\R^n$ with bounded measurable real-valued coefficients and let $W$ be a cylindrical Brownian motion in a Hilbert space $H$. Our main result implies that the stochastic convolution process $$ u(t) = \\int_0^t e^{-(t-s)A}g(s)\\,dW(s), \\quad t\\ge 0,$$ satisfies, for all $1\\le p<\\infty$, a conical maximal $L^p$-regularity estimate $$\\E \\n \\nabla u \\n_{ T_2^{p,2}(\\R_+\\times\\R^n)}^p \\le C_p^p \\E \\n g \\n_{ T_2^{p,2}(\\R_+\\times\\R^n;H)}^p.$$ Here, $T_2^{p,2}(\\R_+\\times\\R^n)$ and $T_2^{p,2}(\\R_+\\times\\R^n;H)$ ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3196","kind":"arxiv","version":3},"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"}