{"paper":{"title":"Regularity estimates in weighted Morrey spaces for quasilinear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giuseppe Di Fazio, Truyen Nguyen","submitted_at":"2018-10-30T02:43:25Z","abstract_excerpt":"We study regularity for solutions of quasilinear elliptic equations of the form $\\div \\A(x,u,\\nabla u) = \\div \\F $ in bounded domains in $\\R^n$. The vector field $\\A$ is assumed to be continuous in $u$, and its growth in $\\nabla u$ is like that of the $p$-Laplace operator. We establish interior gradient estimates in weighted Morrey spaces for weak solutions $u$ to the equation under a small BMO condition in $x$ for $\\A$. As a consequence, we obtain that $\\nabla u$ is in the classical Morrey space $\\calM^{q,\\lambda}$ or weighted space $L^q_w$ whenever $|\\F|^{\\frac{1}{p-1}}$ is respectively in $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12496","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"}