{"paper":{"title":"Sharp weighted Korn and Korn-like inequalities and an application to washers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Davit Harutyunyan","submitted_at":"2015-09-10T03:11:33Z","abstract_excerpt":"In this paper we prove asymptotically sharp weighted \"first-and-a-half\" $2D$ Korn and Korn-like inequalities with a singular weight occurring from Cartesian to cylindrical change of variables. We prove some Hardy and the so-called \"harmonic function gradient separation\" inequalities with the same singular weight. Then we apply the obtained $2D$ inequalities to prove similar inequalities for washers with thickness $h$ subject to vanishing Dirichlet boundary conditions on the inner and outer thin faces of the washer. A washer can be regarded in two ways: As the limit case of a conical shell when"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02994","kind":"arxiv","version":2},"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"}