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Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity

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dc.contributor.author Tealdi, Lucia
dc.contributor.author Bellettini, Giovanni
dc.contributor.author Paolini, Maurizio
dc.date.accessioned 2015-08-10T07:11:45Z
dc.date.available 2015-08-10T07:11:45Z
dc.date.issued 2015-08-07
dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/34483
dc.description The preprint is compsed of 37 pages and is recorded in PDF format en_US
dc.description.abstract We address the problem of estimating the area of the graph of a map u, defined on a bounded planar domain O and taking values in the plane, jumping on a segment J, either compactly contained in O or having both the end points on the boundary of O. We define the relaxation of the area functional w.r.t. a sort of uniform convergence, and we characterize it in terms of the infimum of the area among those surfaces in the space spanning the graphs of the traces of u on the two side of J and having what we have called a semicartesian structure. We exhibit examples showing that the relaxed area functional w.r.t the L^1 convergence may depend also on the values of u far from J, and on the relative position of J w.r.t. the boundary of O; these examples confirm the non-local behaviour of the L^1 relaxed area functional, and justify the interest in studying the relaxation w.r.t. a stronger convergence. We prove also that the L^1 relaxed area functional in non-subadditive for a rather class of maps. en_US
dc.language.iso en en_US
dc.subject area of a graph en_US
dc.subject discontinuous map en_US
dc.subject semicartesian surfaces en_US
dc.subject relaxed area functional en_US
dc.title Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity en_US
dc.type Preprint en_US
dc.subject.miur MAT/05 en_US
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US


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