{"paper":{"title":"Bubbling solutions for nonlocal elliptic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juan D\\'avila, Luis L\\'opez R\\'ios, Yannick Sire","submitted_at":"2014-10-20T20:57:49Z","abstract_excerpt":"We investigate bubbling solutions for the nonlocal equation \\[\n  A_\\Omega^s u =u^p,\\ u >0 \\quad \\mbox{in } \\Omega, \\] under homogeneous Dirichlet conditions, where $\\Omega$ is a bounded and smooth domain. The operator $A_\\Omega^s$ stands for two types of nonlocal operators that we treat in a unified way: either the spectral fractional Laplacian or the restricted fractional Laplacian. In both cases $s \\in (0,1)$ and the Dirichlet conditions are different: for the spectral fractional Laplacian, we prescribe $u=0$ on $\\partial \\Omega$ and for the restricted fractional Laplacian, we prescribe $u=0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5461","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"}