{"paper":{"title":"Surface Riesz transforms and spectral property of elastic Neumann--Poinca\\'e operators on less smooth domains in three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.FA","authors_text":"Daisuke Kawagoe, Hyeonbae Kang","submitted_at":"2018-06-06T06:31:33Z","abstract_excerpt":"It is known that the Neumann--Poincar\\'e operator for the Lam\\'e system of linear elasticity is polynomially compact and, as a consequence, that its spectrum consists of three non-empty sequences of eigenvalues accumulating to certain numbers determined by Lam\\'e parameters, if the boundary of the domain where the operator is defined is $C^\\infty$-smooth. We extend this result to less smooth boundaries, namely, $C^{1, \\alpha}$-smooth boundaries for some $\\alpha > 0$. The results are obtained by proving certain identities for surface Riesz transforms, which are singular integral operators of no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02026","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"}