{"paper":{"title":"The Stokes problem with Navier slip boundary condition: Minimal fractional Sobolev regularity of the domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","math.OC"],"primary_cat":"math.AP","authors_text":"Harbir Antil, Patrick Sodre, Ricardo H. Nochetto","submitted_at":"2015-12-25T00:14:50Z","abstract_excerpt":"We prove well-posedness in reflexive Sobolev spaces of weak solutions to the stationary Stokes problem with Navier slip boundary condition over bounded domains $\\Omega$ of $\\mathbb{R}^n$ of class $W^{2-1/s}_s$, $s>n$. Since such domains are of class $C^{1,1-n/s}$, our result improves upon the recent one by Amrouche-Seloula, who assume $\\Omega$ to be of class $C^{1,1}$. We deal with the slip boundary condition directly via a new localization technique, which features domain, space and operator decompositions. To flatten the boundary of $\\Omega$ locally, we construct a novel $W^2_s$ diffeomorphi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07936","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"}