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On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity

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dc.contributor.author Bellettini, Giovanni
dc.contributor.author Tealdi, Lucia
dc.contributor.author Paolini, Maurizio
dc.date.accessioned 2013-12-02T07:47:43Z
dc.date.available 2013-12-02T07:47:43Z
dc.date.issued 2013-10-09
dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/7224
dc.description This article is composed of 42 pages and was published as preprint at SISSA en_US
dc.description.abstract In this paper we provide an estimate from above for the value of the relaxed area functional for a map defined on a bounded domain of the plane with values in the plane and discontinuous on a regular simple curve with two endpoints. We show that, under suitable assumptions, the relaxed area does not exceed the area of the regular part of the map, with the addition of a singular term measuring the area of a disk type solution of the Plateau's problem spanning the two traces of the map on the jump. The result is valid also when the area minimizing surface has self intersections. A key element in our argument is to show the existence of what we call a semicartesian parametrization of this surface, namely a conformal parametrization defined on a suitable parameter space, which is the identity in the first component. To prove our result, various tools of parametric minimal surface theory are used, as well as some result from Morse theory. en_US
dc.language.iso en en_US
dc.relation.ispartofseries arXiv:1310.2443;
dc.title On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity en_US
dc.type Preprint en_US
dc.subject.keyword Area functional en_US
dc.subject.keyword Area en_US
dc.subject.keyword parametric minimal surfaces en_US
dc.subject.miur MAT/05 ANALISI MATEMATICA
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US


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