{"paper":{"title":"Some interior regularity estimates for solutions of complex Monge-Amp\\`ere equations on a ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CV"],"primary_cat":"math.DG","authors_text":"Chao Li, Jiayu Li, Xi Zhang","submitted_at":"2018-09-21T02:41:25Z","abstract_excerpt":"In this paper, we consider the Dirichlet problem of a complex Monge-Amp\\`ere equation on a ball in $\\mathbb C^n$. With $\\mathcal C^{1,\\alpha}$ (resp. $\\mathcal C^{0,\\alpha}$) data, we prove an interior $\\mathcal C^{1,\\alpha}$ (resp. $\\mathcal C^{0,\\alpha}$) estimate for the solution. These estimates are generalized versions of the Bedford-Taylor interior $\\mathcal C^{1,1}$ estimate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07919","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"}