{"paper":{"title":"Dirichlet-to-Neumann semigroup with respect to a general second order eigenvalue problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"\\'Erika Capelato, Jamil Abreu","submitted_at":"2016-06-13T14:11:59Z","abstract_excerpt":"In this paper we present a preliminary study on the Dirichlet-to-Neumann operator with respect to a second order elliptic operator with measurable coefficients, including first order terms, namely, the operator on $L^2(\\partial\\Omega)$ given by $\\varphi\\mapsto \\partial_{\\nu}u$ where $u$ is a weak solution of \\begin{equation} \\left\\{ \\begin{aligned} -{\\rm div}\\, (a\\nabla u) +b\\cdot \\nabla u -{\\rm div}\\, (cu)+du & =\\lambda u \\ \\ \\text{on}\\ \\Omega,\\\\ u|_{\\partial\\Omega} & =\\varphi . \\end{aligned} \\right. \\end{equation} Under suitable assumptions on the matrix-valued function $a$, on the vector fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03961","kind":"arxiv","version":4},"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"}