{"paper":{"title":"The Boundary value problems for second order elliptic operators satisfying a Carleson condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David Rule, Jill Pipher, Martin Dindo\\v{s}","submitted_at":"2013-01-03T11:47:03Z","abstract_excerpt":"Let $\\Omega$ be a Lipschitz domain in $\\mathbb R^n$ $n\\geq 2,$ and $L=\\mbox{div} (A\\nabla\\cdot)$ be a second order elliptic operator in divergence form. We establish solvability of the Dirichlet regularity problem with boundary data in $H^{1,p}(\\partial\\Omega)$ and of the Neumann problem with $L^p(\\partial\\Omega)$ data for the operator $L$ on Lipschitz domains with small Lipschitz constant. We allow the coefficients of the operator $L$ to be rough obeying a certain Carleson condition with small norm. These results complete the results of [5] where $L^p(\\partial\\Omega)$ Dirichlet problem was co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0426","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":""},"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"}