{"paper":{"title":"Regularity up to the boundary for singularly perturbed fully nonlinear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gleydson C. Ricarte, Jo\\~ao Vitor da Silva","submitted_at":"2015-10-08T03:57:22Z","abstract_excerpt":"In this article we are interested in studying regularity up to the boundary for one-phase singularly perturbed fully nonlinear elliptic problems, associated to high energy activation potentials, namely $$\n  F(X, \\nabla u^{\\varepsilon}, D^2 u^{\\varepsilon}) = \\zeta_{\\varepsilon}(u^{\\varepsilon})\n  \\quad \\mbox{in} \\quad \\Omega \\subset \\R^n $$ where $\\zeta_{\\varepsilon}$ behaves asymptotically as the Dirac measure $\\delta_{0}$ as $\\varepsilon$ goes to zero. We shall establish global gradient bounds independent of the parameter $\\varepsilon$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02193","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"}