{"paper":{"title":"On the strong maximum principle for nonlocal operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sven Jarohs, Tobias Weth","submitted_at":"2017-02-28T12:48:12Z","abstract_excerpt":"In this paper we derive a strong maximum principle for weak supersolutions of nonlocal equations of the form $Iu=c(x) u$ in $\\Omega$, where $\\Omega\\subset \\mathbb{R}^N$ is a domain, $c\\in L^{\\infty}(\\Omega)$ and $I$ is an operator of the form $Iu(x)=P.V.\\int_{\\mathbb{R}^N}(u(x)-u(y))j(x-y)\\ dy$ with a nonnegative kernel function $j$. We formulate minimal positivity assumptions on $j$ corresponding to a class of operators which includes highly anisotropic variants of the fractional Laplacian. Somewhat surprisingly, this problem leads to the study of general lattices in $\\mathbb{R}^N$. Our resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08767","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"}