{"paper":{"title":"A counterexample related to the regularity of the $p$-Stokes problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Martin K\\v{r}epela, Michael R\\r{u}\\v{z}i\\v{c}ka","submitted_at":"2017-11-21T15:14:24Z","abstract_excerpt":"In this paper we construct a solenoidal vector field $\\mathbf{u}$ belonging to $W^{2,q}(\\Omega)\\cap W^{1,s}_0(\\Omega)$, $s \\in (1,\\infty)$, $q \\in (1,n)$, such that $(1+|\\mathbf{Du}|)^{p-2}$, $p\\in (1,2)\\cup(2,\\infty)$, does not belong to the Muckenhoupt class $A_\\infty(\\Omega)$. Thus, one cannot use the Korn inequality in weighted Lebesgue spaces to prove the natural regularity of the $p$-Stokes problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07834","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"}