{"paper":{"title":"The Green function for the Stokes system with measurable coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jongkeun Choi, Ki-Ahm Lee","submitted_at":"2015-03-25T06:16:11Z","abstract_excerpt":"We study the Green function for the stationary Stokes system with bounded measurable coefficients in a bounded Lipschitz domain $\\Omega\\subset \\mathbb{R}^n$, $n\\ge 3$. We construct the Green function in $\\Omega$ under the condition $(\\bf{A1})$ that weak solutions of the system enjoy interior H\\\"older continuity. We also prove that $(\\bf{A1})$ holds, for example, when the coefficients are $\\mathrm{VMO}$. Moreover, we obtain the global pointwise estimate for the Green function under the additional assumption $(\\bf{A2})$ that weak solutions of Dirichlet problems are locally bounded up to the boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07290","kind":"arxiv","version":4},"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"}