{"paper":{"title":"Boundary behavior and interior H\\\"older regularity of solution to nonlinear stochastic partial differential equations driven by space-time white noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Beom-seok Han, Kyeong-Hun Kim","submitted_at":"2019-05-28T04:54:36Z","abstract_excerpt":"We present uniqueness and existence in weighted Sobolev spaces of the equation $$ u_t=(au_{xx}+bu_x+cu)+ \\xi |u|^{1+\\lambda} {\\dot{B}}, \\quad\\,\\, t>0, \\, x\\in (0,1) $$ with initial data $u(0,\\cdot)=u_0$ and zero boundary data. Here $\\lambda\\in [0,1/2)$, $\\dot{B}$ is a space-time white noise, and the coefficients $a,b,c$ and the function $\\xi$ depend on $(\\omega,t,x)$ and the initial data $u_0$ depends on $(\\omega,x)$.\n  More importantly, we obtain various interior H\\\"older regularities and boundary behaviors of the solution. For instance, if the initial data is in appropriate $L_p$ spaces, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11609","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"}