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dc.contributor.author
Chicco Ruiz, Anibal Leonardo
dc.contributor.author
Morin, Pedro
dc.contributor.author
Pauletti, Miguel Sebastian
dc.date.available
2019-08-27T18:52:30Z
dc.date.issued
2018-09
dc.identifier.citation
Chicco Ruiz, Anibal Leonardo; Morin, Pedro; Pauletti, Miguel Sebastian; The shape derivative of the Gauss curvature; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 59; 2; 9-2018; 311-337
dc.identifier.issn
0041-6932
dc.identifier.uri
http://hdl.handle.net/11336/82279
dc.description.abstract
We present a review of results about the shape derivatives of scalar- and vector-valued shape functions, and extend the results from Doğan and Nochetto [ESAIM Math. Model. Numer. Anal. 46 (2012), no. 1, 59-79] to more general surface energies. In that article, Doğan and Nochetto consider surface energies defined as integrals over surfaces of functions that can depend on the position, the unit normal and the mean curvature of the surface. In this work we present a systematic way to derive formulas for the shape derivative of more general geometric quantities, including the Gauss curvature (a new result not available in the literature) and other geometric invariants (eigenvalues of the second fundamental form). This is done for hyper-surfaces in the Euclidean space of any finite dimension. As an application of the results, with relevance for numerical methods in applied problems, we derive a Newton-type method to approximate a minimizer of a shape functional. We finally find the particular formulas for the first and second order shape derivatives of the area and the Willmore functional, which are necessary for the aforementioned Newton-type method.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Unión Matemática Argentina
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Differentiation Formulas
dc.subject
Gauss Curvature
dc.subject
Shape Derivative
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Shape Optimization
dc.subject.classification
Matemática Aplicada
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
The shape derivative of the Gauss curvature
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2019-08-08T20:36:15Z
dc.identifier.eissn
1669-9637
dc.journal.volume
59
dc.journal.number
2
dc.journal.pagination
311-337
dc.journal.pais
Argentina
dc.journal.ciudad
Bahia Blanca
dc.description.fil
Fil: Chicco Ruiz, Anibal Leonardo. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina
dc.description.fil
Fil: Morin, Pedro. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina
dc.description.fil
Fil: Pauletti, Miguel Sebastian. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina
dc.journal.title
Revista de la Unión Matemática Argentina
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/revuma.php?p=doi/v59n2a06
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.33044/revuma.v59n2a06
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