{"paper":{"title":"Optimal $C^{1,\\alpha}$ estimates for a class of elliptic quasilinear equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Damiao Araujo, Lei Zhang","submitted_at":"2015-07-24T15:57:50Z","abstract_excerpt":"In this article we establish sharp $C^{1,\\alpha}$ estimates for weak solutions of singular and degenerate quasilinear elliptic equation $$-\\,div\\, a(x, \\nabla u) = f,$$\n  which includes the standard $p$-laplacean equation with varying coefficients as a special case. The sharp exponent $\\alpha$ is asymptotically optimal and is determined by the H\\\"older regularity of the coefficients, the exponent $p$ and the $q$-integrability of the source term $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06898","kind":"arxiv","version":4},"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"}