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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.11103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-15T08:53:04Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"633ec687984ac4091cbf4b9713adf8d6f702126d95c558faa5b93983361375cb","abstract_canon_sha256":"7460a529661b00d29868c8d3dc63df72167a846068e76087d42436bf41551833"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:37:32.011569Z","signature_b64":"RUTOni2hZNXGLxS5VyyAaxxWD50JsDt3LvgNOKRsQJ7SzFHeXA9208FnBCCXykus7x8b4DUY36nP7Lhk938wBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33884d82659a1d7a394dbaf8e8a02690d6f2b7378db3fe28428d94771cce5fde","last_reissued_at":"2026-07-05T11:37:32.011111Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:37:32.011111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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