{"paper":{"title":"On higher integrability estimates for elliptic equations with singular coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juraj F\\\"oldes, Tuoc Phan","submitted_at":"2018-04-09T18:43:53Z","abstract_excerpt":"In this note we establish existence and uniqueness of weak solutions of linear elliptic equation $\\text{div}[\\mathbf{A}(x) \\nabla u] = \\text{div}{\\mathbf{F}(x)}$, where the matrix $\\mathbf{A}$ is just measurable and its skew-symmetric part can be unbounded. Global reverse H\\\"{o}lder's regularity estimates for gradients of weak solutions are also obtained. Most importantly, we show, by providing an example, that boundedness and ellipticity of $\\mathbf{A}$ is not sufficient for higher integrability estimates even when the symmetric part of $\\mathbf{A}$ is the identity matrix. In addition, the ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03180","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"}