{"paper":{"title":"Boundary $C^{2, \\alpha}$ Regularity for the Oblique Boundary Value Problem of Monge-Amp\\`ere Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huaiyu Jian, Xushan Tu","submitted_at":"2021-11-18T15:50:59Z","abstract_excerpt":"We study the good shape property of boundary sections of convex solutions of the oblique boundary value problem for Monge-Amp\\`ere equations $$\\det D^2u =f(x) \\text{ in } \\Omega , \\quad D_{\\beta}u = \\phi(x) \\text{ on } \\partial \\Omega.$$ In the two-dimensional case, we prove the global $C^{2,\\alpha}$ estimate for the solution. When the dimension $n \\geq 3$, we show that this estimate still holds if the solution is bounded from above by a quadratic function in the tangent direction. We also obtain an existence result for the convex solution of Monge-Amp\\`ere equations with Robin oblique boundar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.09765","kind":"arxiv","version":2},"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/2111.09765/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"}