{"paper":{"title":"Constant rank operators in Korn-Maxwell-Sobolev inequalities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Paul Stephan, Peter Lewintan","submitted_at":"2024-12-19T14:02:17Z","abstract_excerpt":"We focus on Korn-Maxwell-Sobolev inequalities for operators of reduced constant rank. These inequalities take the form \\[ \\|P - \\Pi_{\\mathbb{B}} \\Pi_{\\ker\\mathscr{A}} P\\|_{\\dot{\\mathrm{W}}^{k-1, p^*}(\\mathbb{R}^n)} \\le c \\, (\\|\\mathscr{A}[P]\\|_{\\dot{\\mathrm{W}}^{k-1, p^*}(\\mathbb{R}^n)} + \\|\\mathbb{B} P\\|_{\\mathrm{L}^p(\\mathbb{R}^n)}) \\] for all $ P \\in \\mathrm{C}_c^\\infty(\\mathbb{R}^n; V) $, where $ V $ is a finite-dimensional vector space, $ \\mathscr{A} $ is a linear mapping, and $ \\mathbb{B} $ is a constant coefficient homogeneous differential operator of order $ k $. In particular, we can "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.14866","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.14866/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}