{"paper":{"title":"The Dirichlet-to-Neumann operator via hidden compactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A.F.M. ter Elst, J.B. Kennedy, M. Sauter, W. Arendt","submitted_at":"2013-05-03T14:25:19Z","abstract_excerpt":"We show that to each symmetric elliptic operator of the form \\[ \\mathcal{A} = - \\sum \\partial_k \\, a_{kl} \\, \\partial_l + c \\] on a bounded Lipschitz domain $\\Omega \\subset \\mathbb{R}^d$ one can associate a self-adjoint Dirichlet-to-Neumann operator on $L_2(\\partial \\Omega)$, which may be multi-valued if 0 is in the Dirichlet spectrum of $\\mathcal{A}$. To overcome the lack of coerciveness in this case, we employ a new version of the Lax--Milgram lemma based on an indirect ellipticity property that we call hidden compactness. We then establish uniform resolvent convergence of a sequence of Diri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0720","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":""},"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"}