{"paper":{"title":"Equivalent Characterizations and Their Applications of Solvability of $L^p$ Poisson--Robin(-Regularity) Problems on Rough Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.AP","authors_text":"Dachun Yang, Sibei Yang, Xuelian Fu","submitted_at":"2025-07-15T08:53:04Z","abstract_excerpt":"Let $n\\ge2$, $\\Omega\\subset\\mathbb{R}^n$ be a bounded one-sided chord arc domain, and $p\\in(1,\\infty)$. In this article, we study the (weak) $L^p$ Poisson--Robin(-regularity) problem for a uniformly elliptic operator $L:=-\\mathrm{div}(A\\nabla\\cdot)$ of divergence form on $\\Omega$, which considers weak solutions to the equation $Lu=h-\\mathrm{div}\\boldsymbol{F}$ in $\\Omega$ with the Robin boundary condition $A\\nabla u\\cdot\\boldsymbol{\\nu}+\\alpha u=\\boldsymbol{F}\\cdot\\boldsymbol{\\nu}$ on the boundary $\\partial\\Omega$ for functions $h$ and $\\boldsymbol{F}$ in some tent spaces. Precisely, we establ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.11103","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.11103/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"}