{"paper":{"title":"Pointwise gradient estimates for a class of singular quasilinear equation with measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nguyen Cong Phuc, Quoc-Hung Nguyen","submitted_at":"2019-02-12T14:48:49Z","abstract_excerpt":"Local and global pointwise gradient estimates are obtained for solutions to the quasilinear elliptic equation with measure data $-\\operatorname{div}(A(x,\\nabla u))=\\mu$ in a bounded and possibly nonsmooth domain $\\Omega$ in $\\mathbb{R}^n$. Here $\\operatorname{div}(A(x,\\nabla u))$ is modeled after the $p$-Laplacian. Our results extend earlier known results to the singular case in which $\\frac{3n-2}{2n-1}<p\\leq 2-\\frac{1}{n}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04414","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"}