{"paper":{"title":"Interior and boundary higher integrability of very weak solutions for quasilinear parabolic equations with variable exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jehan Oh, Karthik Adimurthi, Sun-Sig Byun","submitted_at":"2018-02-26T06:14:04Z","abstract_excerpt":"We prove boundary higher integrability for the (spatial) gradient of \\emph{very weak} solutions of quasilinear parabolic equations of the form $$ \\left\\{\n  \\begin{array}{ll} u_t - div \\mathcal{A}(x,t,\\nabla u) = 0 &\\quad \\text{on} \\ \\Omega \\times (-T,T), \\\\ u = 0 &\\quad \\text{on} \\ \\partial \\Omega \\times (-T,T),\n  \\end{array} \\right. $$ where the non-linear structure $\\mathcal{A}(x, t,\\nabla u)$ is modelled after the variable exponent $p(x,t)$-Laplace operator given by $|\\nabla u|^{p(x,t)-2} \\nabla u$. To this end, we prove that the gradients satisfy a reverse H\\\"older inequality near the boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09175","kind":"arxiv","version":1},"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"}