{"paper":{"title":"Very large solutions for the fractional Laplacian: towards a fractional Keller-Osserman condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nicola Abatangelo","submitted_at":"2014-12-19T11:39:07Z","abstract_excerpt":"We look for solutions of $(-\\Delta)^s u+f(u) = 0$ in a bounded smooth domain $\\Omega$, $s\\in(0,1)$, with a strong singularity at the boundary. In particular, we are interested in solutions which are $L^1(\\Omega)$ and higher order with respect to dist$(x,\\partial\\Omega)^{s-1}$. We provide sufficient conditions for the existence of such a solution. Roughly speaking, these functions are the real fractional counterpart of \"large solutions\" in the classical setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6298","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"}