{"paper":{"title":"Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ki-Ahm Lee, Yong-Cheol Kim","submitted_at":"2010-11-16T01:25:34Z","abstract_excerpt":"In this paper, we consider fully nonlinear integro-differential equations with possibly nonsymmetric kernels. We are able to find different versions of Alexandroff-Backelman-Pucci estimate corresponding to the full class $\\cS^{\\fL_0}$ of uniformly elliptic nonlinear equations with $1<\\sigma<2$ (subcritical case) and to their subclass $\\cS^{\\fL_0}_{\\eta}$ with $0<\\sigma\\leq 1$. We show that $\\cS^{\\fL_0}_{\\eta}$ still includes a large number of nonlinear operators as well as linear operators. And we show a Harnack inequality, H\\\"older regularity, and $C^{1,\\alpha}$-regularity of the solutions by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3565","kind":"arxiv","version":3},"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"}