{"paper":{"title":"Regularity estimates for nonlocal Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mouhamed Moustapha Fall","submitted_at":"2017-11-06T22:48:28Z","abstract_excerpt":"We prove H\\\"older regularity estimates up to the boundary for weak solutions $u$ to nonlocal Schr\\\"odinger equations subject to exterior Dirichlet conditions in an open set $\\Omega\\subset \\mathbb{R}^N$. The class of nonlocal operators considered here are defined, via Dirichlet forms, by kernels $K(x,y)$ bounded from above and below by $|x-y|^{N+2s}$, with $s\\in (0,1)$. The entries in the equations are in some Morrey spaces and the underline domain $\\Omega$ satisfies some mild regularity assumptions. In the particular case of the fractional Laplacian, our results are new. When $K$ defines a non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02206","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"}