Ibort Latre, Luis AlbertoLledó Macau, FernandoPérez Pardo, Juan Manuel2016-07-182017-02-022015-02-01Journal of Functional Analysis, 2015, v. 268. Issue 3, pp. 634-6700022-1236https://hdl.handle.net/10016/23360We construct in this article a class of closed semi-bounded quadratic forms on the space of square integrable functions over a smooth Riemannian manifold with smooth compact boundary. Each of these quadratic forms specifies a semibounded self-adjoint extension of the Laplace-Beltrami operator. These quadratic forms are based on the Lagrange boundary form on the manifold and a family of domains parametrized by a suitable class of unitary operators on the boundary that will be called admissible. The corresponding quadratic forms are semi-bounded below and closable. Finally, the representing operators correspond to semi-bounded self-adjoint extensions of the Laplace-Beltrami operator. This family of extensions is compared with results existing in the literature and various examples and applications are discussed.38application/pdfeng© Elsevier 2015Atribución-NoComercial-SinDerivadas 3.0 EspañaSelf-adjoint extensionsLaplace-Beltrami operatorQuadratic formsBoundary conditionsresearch articleMatemáticas10.1016/j.jfa.2014.10.013open access6343670Journal of functional analysis268AR/0000016241