{"paper":{"title":"Sharp gradient estimates for quasilinear elliptic equations with $p(x)$ 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":"2017-07-09T07:36:40Z","abstract_excerpt":"In this paper, we study quasilinear elliptic equations with the nonlinearity modelled after the $p(x)$-Laplacian on nonsmooth domains and obtain sharp Calder\\'on-Zygmund type estimates in the variable exponent setting. In a recent work of \\cite{BO}, the estimates obtained were strictly above the natural exponent and hence there was a gap between the natural energy estimates and estimates above $p(x)$, see \\eqref{energy_introduction} and \\eqref{byun_ok_estimate}. Here, we bridge this gap to obtain the end point case of the estimates obtained in \\cite{BO}, see \\eqref{our_estimate}. In order to d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02535","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"}