{"paper":{"title":"[Regularity of interfaces for a Pucci type segregation problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luis Caffarelli, Monica Torres, Stefania Patrizi, Veronica Quitalo","submitted_at":"2018-03-09T00:03:36Z","abstract_excerpt":"We show the existence of a Lipschitz viscosity solution $u$ in $\\Omega$ to a system of fully nonlinear equations involving Pucci-type operators. We study the regularity of the interface $\\partial \\{ u> 0 \\}\\cap\\Om$ and we show that the viscosity inequalities of the system imply, in the weak sense, the free boundary condition $u^{+}_{\\nu_{+}} = u^{-}_{\\nu_{-}}$, and hence $u$ is a solution to a two-phase free boundary problem. We show that we can apply the classical method of sup-convolutions developed by the first author in \\cite{caffarelli_harnack_1987,caffarelli_harnack_1989}, and generalize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03337","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"}