{"paper":{"title":"On a Class of Nonlocal Obstacle Type Problems Related to the Distributional Riesz Fractional Derivative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Catharine W.K. Lo, Jos\\'e Francisco Rodrigues","submitted_at":"2021-01-18T03:39:12Z","abstract_excerpt":"In this work, we consider the nonlocal obstacle problem with a given obstacle $\\psi$ in a bounded Lipschitz domain $\\Omega$ in $\\mathbb{R}^{d}$, such that $\\mathbb{K}_\\psi^s=\\{v\\in H^s_0(\\Omega):v\\geq\\psi \\text{ a.e. in }\\Omega\\}\\neq\\emptyset$, given by \\[u\\in\\mathbb{K}_\\psi^s:\\langle\\mathcal{L}_au,v-u\\rangle\\geq\\langle F,v-u\\rangle\\quad\\forall v\\in\\mathbb{K}^s_\\psi,\\] for $F\\in H^{-s}(\\Omega)$, the dual space of $H^s_0(\\Omega)$, $0<s<1$. The nonlocal operator $\\mathcal{L}_a:H^s_0(\\Omega)\\to H^{-s}(\\Omega)$ is defined with a measurable, bounded, strictly positive singular kernel $a(x,y)$, poss"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.06863","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2101.06863/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}