{"paper":{"title":"Global Lorentz and Lorentz-Morrey estimates below the natural exponent for quasilinear equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Karthik Adimurthi, Nguyen Cong Phuc","submitted_at":"2014-12-15T23:23:12Z","abstract_excerpt":"Lorentz and Lorentz-Morrey estimates are obtained for gradients of very weak solutions to quasilinear equations of the form $$\\text{div}\\,\\mathcal{A}(x, \\nabla u)=\\text{div}\\, |{\\bf f}|^{p-2}{\\bf f},$$ where $\\text{div}\\,\\mathcal{A}(x, \\nabla u)$ is modelled after the $p$-Laplacian, $p>1$. The estimates are global over bounded domains that satisfy a mild exterior uniform thickness condition that involves the $p$-capacity. The vector field datum ${\\bf f}$ is allowed to have low degrees of integrability and thus solutions may not have finite $L^p$ energy. A higher integrability result at the bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4833","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"}