{"paper":{"title":"Uniform Equicontinuity for a family of Zero Order operators approaching the fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Erwin Topp (LMPT), Patricio Felmer (DIM)","submitted_at":"2014-05-13T19:15:28Z","abstract_excerpt":"In this paper we consider a smooth bounded domain $\\Omega \\subset \\R^N$ and a parametric family of radially symmetric kernels $K_\\epsilon: \\R^N \\to \\R_+$ such that, for each $\\epsilon \\in (0,1)$, its $L^1-$norm is finite but it blows up as $\\epsilon \\to 0$. Our aim is to establish an $\\epsilon$ independent modulus of continuity in ${\\Omega}$, for the solution $u_\\epsilon$ of the homogeneous Dirichlet problem \\begin{equation*} \\left \\{ \\begin{array}{rcll} - \\I_\\epsilon [u] \\&=\\& f \\& \\mbox{in} \\ \\Omega. \\\\ u \\&=\\& 0 \\& \\mbox{in} \\ \\Omega^c, \\end{array} \\right . \\end{equation*} where $f \\in C(\\b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3261","kind":"arxiv","version":2},"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"}