{"paper":{"title":"Sobolev versus H\\\"older minimizers for the degenerate fractional $p$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Iannizzotto, Marco Squassina, Sunra Mosconi","submitted_at":"2019-07-20T13:52:36Z","abstract_excerpt":"We consider a nonlinear pseudo-differential equation driven by the fractional $p$-Laplacian $(-\\Delta)^s_p$ with $s\\in(0,1)$ and $p\\ge 2$ (degenerate case), under Dirichlet type conditions in a smooth domain $\\Omega$. We prove that local minimizers of the associated energy functional in the fractional Sobolev space $W^{s,p}_0(\\Omega)$ and in the weighted H\\\"older space $C^0_s(\\overline\\Omega)$, respectively, do coincide."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08814","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"}