EXPLICIT VARIATIONAL FORMS FOR THE INVERSES OF INTEGRAL LOGARITHMIC OPERATORS OVER AN INTERVAL

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dc.contributor.authorJerez Hanckes, Carlos
dc.contributor.authorNedelec, Jean Claude
dc.date.accessioned2024-01-10T12:05:24Z
dc.date.available2024-01-10T12:05:24Z
dc.date.issued2012
dc.description.abstractWe introduce explicit and exact variational formulations for the weakly singular and hypersingular operators over an open interval as well as for their corresponding inverses. Contrary to the case of a closed curve, these operators no longer map fractional Sobolev spaces in a dual fashion but degenerate into different subspaces depending on their extensibility by zero. We show that an average and jump decomposition leads to precise coercivity results and characterize the mismatch occurring between associated functional spaces. Through this setting, we naturally define Calderon-type identities with their potential use as preconditioners. Moreover, we provide an interesting relation between the logarithmic operators and one-dimensional Laplace Dirichlet and Neumann problems. This work is a detailed and extended version of the article "Variational Forms for the Inverses of Integral Logarithmic Operators over an Interval" by Jerez-Hanckes and Nedelec [C. R. Acad. Sci. Paris Ser. I, 349 (2011), pp. 547-552].
dc.description.funderETH Zurich Postdoctoral Fellowship
dc.fechaingreso.objetodigital2024-05-14
dc.format.extent29 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1137/100806771
dc.identifier.eissn1095-7154
dc.identifier.issn0036-1410
dc.identifier.urihttps://doi.org/10.1137/100806771
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/76001
dc.identifier.wosidWOS:000310137800018
dc.information.autorucIngeniería;Jerez C;S/I;14773
dc.issue.numero4
dc.language.isoen
dc.nota.accesocontenido parcial
dc.pagina.final2694
dc.pagina.inicio2666
dc.publisherSIAM PUBLICATIONS
dc.revistaSIAM JOURNAL ON MATHEMATICAL ANALYSIS
dc.rightsacceso restringido
dc.subjectopen surface problems
dc.subjectintegral logarithmic equations
dc.subjectboundary integral equations
dc.subjectLaplace equation
dc.subjectCalderon projectors
dc.subjectNUMERICAL-SOLUTION
dc.subjectCHEBYSHEV POLYNOMIALS
dc.subjectEQUATION
dc.subjectCOLLOCATION
dc.subjectSINGULARITIES
dc.subjectSCREEN
dc.titleEXPLICIT VARIATIONAL FORMS FOR THE INVERSES OF INTEGRAL LOGARITHMIC OPERATORS OVER AN INTERVAL
dc.typeartículo
dc.volumen44
sipa.codpersvinculados14773
sipa.indexWOS
sipa.indexScopus
sipa.trazabilidadCarga SIPA;09-01-2024
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