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Suppose $\\Omega\\subset\\subset \\mathbb R^n$ is uniformly convex and analytic. Then the solution of the degenerate Monge-Amp\\`ere equation is analytic in $\\bar\\Omega$ provided $q\\in \\mathbb Z^+$."},"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":"2012.02656","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2020-12-04T15:31:45Z","cross_cats_sorted":[],"title_canon_sha256":"c0fe9eef8430c68d00cf6bc0b9eadb03a680365f2a5371d3db0d906bfd2e548b","abstract_canon_sha256":"3f13bd08c51af9e201ecb7d5c8a88bbc0f6041b4bae42d9a073d4994272fa244"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:57:08.957045Z","signature_b64":"FA+6EyGvJsC56UuP5wA5XZM/5Mh0zSEX1IpmelCqO/Pnu4goI8uy4JF4Rrddn/8oAFcdVRNdaOo4XksMUFO6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a19178ad83cfce616d6ce14850d15cdab24f510838bc33c4b15b94ae28c21241","last_reissued_at":"2026-07-05T01:57:08.956711Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:57:08.956711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analyticity of the solutions to degenerate Monge-Amp\\`ere equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Genggeng Huang, Yingshu L\\\"u","submitted_at":"2020-12-04T15:31:45Z","abstract_excerpt":"This paper is devoted to study the following degenerate Monge-Amp\\`ere equation: \\begin{eqnarray}\\label{ab1} \\begin{cases} \\det D^2 u=\\Lambda_q (-u)^q \\quad \\text{in}\\quad \\Omega,\\\\ u=0 \\quad\\text{on}\\quad \\partial\\Omega \\end{cases} \\end{eqnarray} for some positive constant $\\Lambda_q$. Suppose $\\Omega\\subset\\subset \\mathbb R^n$ is uniformly convex and analytic. 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