{"paper":{"title":"Optimal gradient continuity for degenerate elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Dami\\~ao J. Ara\\'ujo, Eduardo V. Teixeira, Gleydson C. Ricarte","submitted_at":"2012-06-18T22:08:27Z","abstract_excerpt":"We establish new, optimal gradient continuity estimates for solutions to a class of 2nd order partial differential equations, $\\mathscr{L}(X, \\nabla u, D^2 u) = f$, whose diffusion properties (ellipticity) degenerate along the \\textit{a priori} unknown singular set of an existing solution, $\\mathscr{S}(u) := \\{X : \\nabla u(X) = 0 \\}$. The innovative feature of our main result concerns its optimality -- the sharp, encoded smoothness aftereffects of the operator. Such a quantitative information usually plays a decisive role in the analysis of a number of analytic and geometric problems. Our resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4089","kind":"arxiv","version":3},"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"}