{"paper":{"title":"Equivalence of solutions to fractional $p$-Laplace type equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Erik Lindgren, Janne Korvenp\\\"a\\\"a, Tuomo Kuusi","submitted_at":"2016-05-11T14:23:14Z","abstract_excerpt":"In this paper, we study different notions of solutions of nonlocal and nonlinear equations of fractional $p$-Laplace type $${\\rm P.V.} \\int_{\\mathbb R^n}\\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{n+sp}}\\,dy = 0.$$ Solutions are defined via integration by parts with test functions, as viscosity solutions or via comparison. Our main result states that for bounded solutions, the three different notions coincide."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03455","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"}