{"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. Then the solution of the degenerate Monge-Amp\\`ere equation is analytic in $\\bar\\Omega$ provided $q\\in \\mathbb Z^+$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.02656","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.02656/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}