{"paper":{"title":"End point gradient estimates for quasilinear parabolic equations with variable exponent growth on nonsmooth domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jung-Tae Park, Karthik Adimurthi, Sun-Sig Byun","submitted_at":"2018-06-04T04:03:44Z","abstract_excerpt":"In this paper, we study quasilinear parabolic equations with the nonlinearity structure modeled after the $p(x,t)$-Laplacian on nonsmooth domains. The main goal is to obtain end point Calder\\'on-Zygmund type estimates in the variable exponent setting. In a recent work \\cite{byun2016nonlinear}, the estimates obtained were strictly above the natural exponent $p(x,t)$ and hence there was a gap between the natural energy estimates and the estimates above $p(x,t)$ (see \\eqref{energy} and \\eqref{byunok}). Here, we bridge this gap to obtain the end point case of the estimates obtained in \\cite{byun20"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00944","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"}