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Since our \"stress tensor\" is given by means of $\\nabla u $ and not by its symmetric part, then our system is not a $p$-Stokes system. Hence, the system is called {\\it modified} $p$-Stokes system. We look for the high regularity of the solutions $(u,\\pi)$, that is $D^2u,\\nabla\\pi \\in L^q,q\\in(1,\\infty)$. In particular, we get $\\nabla u,\\pi\\in C^{0,\\alpha}$. As far as we know, such a result of high regularity is th"},"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":"1308.0980","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-05T13:36:23Z","cross_cats_sorted":[],"title_canon_sha256":"ed13e977fa87d8df898f04db4a3b02143a93c47ac0e1c30d2968475f11b87f81","abstract_canon_sha256":"26cced2c16dc13926ecd6e8e94acd18face5f53487e3dd4cb1781a0647cc15e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:41.004045Z","signature_b64":"vCrkE2MDS3434s/BP6G5Y7sDu0YbTZPnw4BfiEZORpHgydxaVlmmNzltyHumiNjyuYHaPgwlIgXyxAaEFb70AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"256726d07c76ca3665ed8a14a6daa7604d1f073134584723542b6630837b1930","last_reissued_at":"2026-05-18T03:16:41.003257Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:41.003257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A high regularity result of solutions to modified p-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca Crispo, Paolo Maremonti","submitted_at":"2013-08-05T13:36:23Z","abstract_excerpt":"This paper is concerned with a special elliptic system, which can be seen as a perturbed $p$-Laplacean system, $p\\in(1,2)$, and, for its \"shape\", it is close to the $p$-Stokes system. 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