{"paper":{"title":"The effect of the Hardy potential in some Calder\\'on-Zygmund properties for the fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ana Primo, Boumediene Abdellaoui, Ireneo Peral, Mar\\'ia Medina","submitted_at":"2015-10-29T08:54:05Z","abstract_excerpt":"The goal of this paper is to study the effect of the Hardy potential on the existence and summability of solutions to a class of nonlocal elliptic problems $$ \\left\\{\\begin{array}{rcll} (-\\Delta)^s u-\\lambda \\dfrac{u}{|x|^{2s}}&=&f(x,u) &\\hbox{ in } \\Omega,\\\\ u&=&0 &\\hbox{ in } \\mathbb{R}^N\\setminus\\Omega,\\\\ u&>&0 &\\hbox{ in }\\Omega, \\end{array}\\right. $$ where $(-\\Delta)^s$, $s\\in(0,1)$, is the fractional laplacian operator, $\\Omega\\subset \\mathbb{R}^N$ is a bounded domain with Lipschitz boundary such that $0\\in\\Omega$ and $N>2s$. We will mainly consider the solvability in two cases:\n  1) The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08604","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"}