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Thus, one cannot use the Korn inequality in weighted Lebesgue spaces to prove the natural regularity of the $p$-Stokes problem."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1711.07834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-21T15:14:24Z","cross_cats_sorted":[],"title_canon_sha256":"c8c6cedb0e64ca2d43b0dc3de5b6232db93da113fb10c7651895cf64efa67527","abstract_canon_sha256":"48db281f0f08535fe0837491069128f08299722aeb181fe600e1718c059dfc9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:56.390711Z","signature_b64":"YZwiDMXmapuiWkX1yLxI7+gVTpmnjhvR+j4H1Y7J7LxhzAtnqcCBUxNweN7v4Nn2U9H3bQrR58ONdGKVu49PCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"baa6cda81a00376b06b8f5e19e1093a8c8ab1ab68a79e0164bdcdbbe6dfa5512","last_reissued_at":"2026-05-18T00:29:56.390165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:56.390165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $A_\\infty(\\Omega)$. 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