{"paper":{"title":"Uniform $W^{1,p}$ estimate for elliptic operator with Robin boundary condition in $\\mathcal{C}^1$ domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amrita Ghosh, Carlos Conca, Cherif Amrouche, Tuhin Ghosh","submitted_at":"2018-05-24T06:19:50Z","abstract_excerpt":"We consider the Robin boundary value problem $\\mathrm{div} (A \\nabla u) = \\mathrm{div} \\mathbf{f}+F$ in $\\Omega$, $\\mathcal{C}^1$ domain, with $(A \\nabla u - \\mathbf{f})\\cdot \\mathbf{n} + \\alpha u = g$ on $\\Gamma$, where the matrix $A$ belongs to $VMO (\\mathbb{R}^3) $, and discover the uniform estimates on $\\|u\\|_{W^{1,p}(\\Omega)}$, with $1 < p < \\infty$, independent on $\\alpha$. At the difference with the case $p = 2,$ which is simpler, we call here the weak reverse H\\\"older inequality. This estimates show that the solution of Robin problem converges strongly to the solution of Dirichlet (res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09519","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":""},"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"}