{"paper":{"title":"A relation between the Dirichlet and the Regularity problem for Parabolic equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Erika Nystr\\\"om, Martin Dindo\\v{s}","submitted_at":"2024-09-13T21:19:22Z","abstract_excerpt":"We study the relationship between the Dirichlet and Regularity problem for parabolic operators of the form $ L = \\mbox{div}(A\\nabla\\cdot) - \\partial_t $ on cylindrical domains $ \\Omega = \\mathcal O \\times \\mathbb R $, where the base $ \\mathcal O \\subset \\mathbb R^{n} $ is a $1$-sided chord arc domain (and for one result Lipschitz) in the spatial variables.\n  In the paper we answer the question when the solvability of the $L^p$ Regularity problem for $L$ (denoted by $ (R_L)_{p} $) can be deduced from the solvability of the $ L^{p'} $ Dirichlet problem for the adjoint operator $L^*$ (denoted $ ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.09197","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/2409.09197/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"}