{"paper":{"title":"The Poisson equation from non-local to local","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Umberto Biccari, V\\'ictor Hern\\'andez-Santamar\\'ia","submitted_at":"2018-01-29T12:26:33Z","abstract_excerpt":"We analyze the limit behavior as $s\\to 1^-$ of the solution to the fractional Poisson equation $(-\\Delta)^s u_s=f_s$, $x\\in\\Omega$ with homogeneous Dirichlet boundary conditions $u_s\\equiv 0$, $x\\in\\Omega^c$. We show that $\\lim_{s\\to 1^-} u_s =u$, with $-\\Delta u =f$, $x\\in\\Omega$ and $u=0$, $x\\in\\partial\\Omega$. Our results are complemented by a discussion on the rate of convergence and on extensions to the parabolic setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09470","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"}