{"paper":{"title":"Continuous solutions for divergence-type equations associated to elliptic systems of complex vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Laurent Moonens (LM-Orsay), Tiago Picon","submitted_at":"2017-01-11T08:46:22Z","abstract_excerpt":"In this paper, we characterize all the distributions $F \\in \\mathcal{D}'(U)$ such that there exists a continuous weak solution $v \\in C(U,\\mathbb{C}^{n})$ (with $U \\subset \\Omega$) to the divergence-type equation $$L_{1}^{*}v_{1}+...+L_{n}^{*}v_{n}=F,$$ where  $\\left\\{L_{1},\\dots,L_{n}\\right\\}$ is an elliptic system of linearly independent vector fields with smooth complex coefficients defined on $\\Omega \\subset \\mathbb{R}^{N}$. In case where $(L_1,\\dots, L_n)$ is the usual gradient field on $\\mathbb{R}^N$, we recover the classical result for the divergence equation proved by T. De Pauw and W."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02889","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"}