{"paper":{"title":"Green's function for elliptic systems: existence and Delmotte-Deuschel bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Arianna Giunti, Felix Otto, Joseph G. Conlon","submitted_at":"2016-02-17T23:00:14Z","abstract_excerpt":"We prove that for an open domain $D \\subset \\mathbb{R}^d $ with $d \\geq 2 $ , for every (measurable) uniformly elliptic tensor field $a$ and for almost every point $y \\in D$ , there exists a unique Green's function centred in $ y $ associated to the vectorial operator $ -\\nabla \\cdot a\\nabla $ in D. In particular, when $d > 2$ this result also implies the existence of the fundamental solution for elliptic systems, i.e. the Green function for $ -\\nabla \\cdot a\\nabla $ in $ \\mathbb{R}^d $. Moreover, introducing an ensemble $\\langle\\cdot \\rangle$ over the set of uniformly elliptic tensor fields, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05625","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"}