{"paper":{"title":"Regularity theory and Green's function for elliptic equations with lower order terms in unbounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mihalis Mourgoglou","submitted_at":"2019-04-09T15:03:35Z","abstract_excerpt":"We consider elliptic operators in divergence form with lower order terms of the form $Lu=-$div$\\nabla u+bu)-c\\nabla u-du$, in an open set $\\Omega\\subset \\mathbb{R}^n$, $n\\geq 3$, with possibly infinite Lebesgue measure. We assume that the $n\\times n$ matrix $A$ is uniformly elliptic with real, merely bounded and possibly non-symmetric coefficients, and either $b,c\\in L^{n,\\infty}_{loc}(\\Omega)$ and $d\\in L_{loc}^{\\frac{n}{2},\\infty}(\\Omega)$, or $|b|^2,|c|^2,|d|\\in \\mathcal{K}_{loc}(\\Omega)$, where $\\mathcal{K}_{loc}(\\Omega)$ stands for the local Stummel-Kato class. Let $\\mathcal{K}_{Dini}(\\Om"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04722","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1904.04722/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}