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Le, Ovidiu Savin","submitted_at":"2015-04-03T19:24:43Z","abstract_excerpt":"We obtain $C^{2,\\beta}$ estimates up to the boundary for solutions to degenerate Monge-Amp\\`ere equations of the type $$ \\det D^2 u = f~~\\text{in}~\\Omega, \\quad \\quad ~f\\sim \\text{dist}^{\\alpha}(\\cdot, \\partial\\Omega)~\\text{near}~\\partial\\Omega,~\\alpha>0. $$ As a consequence we obtain global $C^\\infty$ estimates up to the boundary for the eigenfunctions of the Monge-Amp\\`ere operator $(\\det D^2 u)^{1/n}$ on smooth, bounded, uniformly convex domains in $R^n$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1504.00912","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T19:24:43Z","cross_cats_sorted":[],"title_canon_sha256":"56318ba4bfb1d25ff00ca77f70b527e8e307eb390e96ea562edce4bba28ddcba","abstract_canon_sha256":"d29a36b080651fcec3c1aac1693a622375f523388b6bded75aff0b9079516eb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:33.643941Z","signature_b64":"3K0Zisz+WlzwQKFnRbLjDPtzl/SJ+J4Ehw2OaPf9BTIxkpnyo4L/t3ZsQdp0mbhCfydm6Blb7YMpgiMLgg0rAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59ec78e1d7507e0d830e42b2d61ed5ef43a322bd3019695e005c331f2cbd7e9d","last_reissued_at":"2026-05-18T01:11:33.643536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:33.643536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Schauder estimates for degenerate Monge-Amp\\`ere equations and smoothness of the eigenfunctions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nam Q. 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