{"paper":{"title":"Solvability of the Neumann problem for elliptic equations in chord-arc domains with very big pieces of good superdomains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mihalis Mourgoglou, Xavier Tolsa","submitted_at":"2024-07-29T19:21:50Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}^{n+1}$ be a bounded chord-arc domain, let $\\mathcal L=-{\\rm div} A\\nabla$ be an elliptic operator in $\\Omega$ associated with a matrix $A$ having Dini mean oscillation coefficients, and let $1<p\\leq 2$. In this paper we show that if the regularity problem for $\\mathcal L$ is solvable in $L^q$ for some $q>p$ in $\\Omega$, $\\partial \\Omega$ supports a weak $p$-Poincar\\'e inequality, and $\\Omega$ has very big pieces of superdomains for which the Neumann problem for $\\mathcal L$ is solvable uniformly in $L^q$, then the Neumann problem for $\\mathcal L$ is solvable in $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.20385","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.20385/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"}