{"paper":{"title":"Boundary H\\\"older gradient estimates for the Monge-Amp\\`ere equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ovidiu Savin, Qian Zhang","submitted_at":"2018-10-25T02:09:39Z","abstract_excerpt":"We investigate global H\\\"older gradient estimates for solutions to the Monge-Amp\\`ere equation $$\\mathrm{det}\\;D^2 u=f\\quad\\mathrm{in}\\;\\Omega,$$ where the right-hand side $f$ is bounded away from $0$ and $\\infty$. We consider two main situations when a) the domain $\\Omega$ is uniformly convex and b) $\\Omega$ is flat."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10688","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"}