{"paper":{"title":"Regularity for fully nonlinear integro-differential operators with kernels of variable orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ki-Ahm Lee, Minhyun Kim","submitted_at":"2018-05-21T09:16:41Z","abstract_excerpt":"We consider fully nonlinear elliptic integro-differential operators with kernels of variable orders, which generalize the integro-differential operators of the fractional Laplacian type in \\cite{CS}. Since the order of differentiability of the kernel is not characterized by a single number, we use the constant \\begin{align*} C_\\varphi = \\left( \\int_{\\mathbb{R}^n} \\frac{1-\\cos y_1}{\\vert y \\vert^n \\varphi (\\vert y \\vert)} \\, dy \\right)^{-1} \\end{align*} instead of $2-\\sigma$, where $\\varphi$ satisfies a weak scaling condition. We obtain the uniform Harnack inequality and H\\\"older estimates of v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07955","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"}