{"paper":{"title":"Boundary regularity for nonlocal operators with kernels of variable orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jaehun Lee, Ki-Ahm Lee, Minhyun Kim, Panki Kim","submitted_at":"2018-04-05T08:06:56Z","abstract_excerpt":"We study the boundary regularity of solutions of the Dirichlet problem for the nonlocal operator with a kernel of variable orders. Since the order of differentiability of the kernel is not represented by a single number, we consider the generalized H\\\"older space. We prove that there exists a unique viscosity solution of $Lu = f$ in $D$, $u=0$ in $\\mathbb{R}^n \\setminus D$, where $D$ is a bounded $C^{1,1}$ open set, and that the solution $u$ satisfies $u \\in C^V(D)$ and $u/V(d_D) \\in C^\\alpha (D)$ with the uniform estimates, where $V$ is the renewal function and $d_D(x) = \\mbox{dist}(x, \\parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01716","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"}