{"paper":{"title":"Sobolev space theory and H\\\"older estimates for the stochastic partial differential equations on conic and polygonal domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jinsol Seo, Kijung Lee, Kyeong-Hun Kim","submitted_at":"2021-03-29T06:55:36Z","abstract_excerpt":"We establish existence, uniqueness, and Sobolev and H\\\"older regularity results for the stochastic partial differential equation $$ du=\\left(\\sum_{i,j=1}^d a^{ij}u_{x^ix^j}+f^0+\\sum_{i=1}^d f^i_{x^i}\\right)dt+\\sum_{k=1}^{\\infty}g^kdw^k_t, \\quad t>0, \\,x\\in \\mathcal{D} $$ given with non-zero initial data. Here $\\{w^k_t: k=1,2,\\cdots\\}$ is a family of independent Wiener processes defined on a probability space $(\\Omega, \\mathbb{P})$, $a^{ij}=a^{ij}(\\omega,t)$ are merely measurable functions on $\\Omega\\times (0,\\infty)$, and $\\mathcal{D}$ is either a polygonal domain in $\\mathbb{R}^2$ or an arbit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.15372","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.15372/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}