{"paper":{"title":"Interior C^{1,1} regularity of solutions to degenerate Monge-Amp\\`{e}re type equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Feida Jiang, Juhua Shi, Xiaoping Yang","submitted_at":"2018-06-05T14:39:21Z","abstract_excerpt":"In this paper, we study the interior C^{1,1} regularity of viscosity solutions for a degenerate Monge-Amp\\`{e}re type equation \\det[D^{2}u-A(x, u, Du)]=B(x, u, Du) when B \\geq 0 and B^{\\frac{1}{n-1}}\\in C^{1,1}(\\bar{\\Omega}\\times\\mathbb{R}\\times \\mathbb{R}^n). We prove that u\\in C^{1,1}(\\Omega) under the A3 condition and A3w^+ condition respectively. In the former case, we construct a suitable auxiliary function to obtain uniform {\\it a priori} estimates directly. In the latter case, the main argument is to establish the Pogorelov type estimates, which are interesting independently."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01720","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"}