{"paper":{"title":"Some remarks on the duality method for Integro-Differential equations with measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesco Petitta","submitted_at":"2014-09-30T10:22:47Z","abstract_excerpt":"We deal with existence, uniqueness, and regularity for solutions of the boundary value problem\n  $$ \\begin{cases} {\\mathcal L}^s u = \\mu &\\quad \\text{in $\\Omega$}, u(x)=0 \\quad &\\text{on} \\ \\ \\mathbb{R}^N\\backslash\\Omega, \\end{cases} $$ where $\\Omega$ is a bounded domain of $\\mathbb{R}^N$, $\\mu$ is a bounded radon measure on $\\Omega$, and ${\\mathcal L}^s$ is a nonlocal operator of fractional order $s$ whose kernel $K$ is comparable with the one of the factional laplacian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8463","kind":"arxiv","version":3},"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"}