{"paper":{"title":"Limiting Korn-Maxwell-Sobolev inequalities for general incompatibilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Franz Gmeineder, Jean Van Schaftingen, Peter Lewintan","submitted_at":"2024-05-16T06:49:18Z","abstract_excerpt":"We give sharp conditions for the limiting Korn-Maxwell-Sobolev inequalities \\begin{align*}\n  \\lVert P\\rVert_{{\\dot{W}}{^{k-1,\\frac{n}{n-1}}}(\\mathbb{R}^n)}\\le c\\big(\\lVert\\mathscr{A}[P]\\rVert_{{\\dot{W}}{^{k-1,\\frac{n}{n-1}}}(\\mathbb{R}^n)}+\\lVert\\mathbb{B}P\\rVert_{L^{1}(\\mathbb{R}^n)}\\big)\n  \\end{align*} to hold for all $P\\in C_{c}^{\\infty}(\\mathbb{R}^{n};V)$, where $\\mathscr{A}$ is a linear map between finite dimensional vector spaces and $\\mathbb{B}$ is a $k$-th order, linear and homogeneous constant-coefficient differential operator. By the appearance of the $L^{1}$-norm of the differential"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.10349","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/2405.10349/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"}