Self-adjoint extensions of the Laplace&-Beltrami operator and unitaries at the boundary

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dc.contributor.author Ibort Latre, Luis Alberto
dc.contributor.author Lledó Macau, Fernando
dc.contributor.author Pérez Pardo, Juan Manuel
dc.date.accessioned 2016-07-18T10:22:36Z
dc.date.available 2017-02-02T23:00:06Z
dc.date.issued 2015-02-01
dc.identifier.bibliographicCitation Journal of Functional Analysis, 2015, v. 268. Issue 3, pp. 634-670
dc.identifier.issn 0022-1236
dc.identifier.uri http://hdl.handle.net/10016/23360
dc.description.abstract We 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.
dc.description.sponsorship The first and third name authors are partly supported by the project MTM2010-21186-C02-02 of the Spanish Ministerio de Ciencia e Innovación and QUITEMAD programme P2009 ESP-1594. The second-named author was partially supported by projects DGI MICIIN MTM2012-36372-C03-01 and Severo Ochoa SEV-2011-0087 of the Spanish Ministry of Economy and Competition. The third-named author was also partially supported in 2011 and 2012 by mobility grants of the “Universidad Carlos III de Madrid”.
dc.format.extent 38
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Elsevier
dc.rights © Elsevier 2015
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Self-adjoint extensions
dc.subject.other Laplace-Beltrami operator
dc.subject.other Quadratic forms
dc.subject.other Boundary conditions
dc.title Self-adjoint extensions of the Laplace&-Beltrami operator and unitaries at the boundary
dc.type article
dc.relation.publisherversion http://dx.doi.org/10.1016/j.jfa.2014.10.013
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1016/j.jfa.2014.10.013
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2010-21186-C02-02
dc.relation.projectID Gobierno de España. P2009 ESP-1594
dc.relation.projectID Gobierno de España. MTM2012-36372-C03-01
dc.relation.projectID Gobierno de España. SEV-2011-0087
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 634
dc.identifier.publicationissue 3
dc.identifier.publicationlastpage 670
dc.identifier.publicationtitle Journal of functional analysis
dc.identifier.publicationvolume 268
dc.identifier.uxxi AR/0000016241
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