Tealdi, Lucia
The relaxed area of maps from the plane to the plane with a line discontinuity, and the role of semicartesian surfaces. [Tesi di dottorato]
SISSA, 2015-09-25
In this thesis we study the relaxation of the area functional w.r.t. the L^1 topology of a map from a bounded planar domain with values in the plane and jumping on a segment. We estimate from above the singular contribution of this functional due to the presence of the jump in terms of the infimum of the area among a suitable family of surfaces that we call semicartesian surfaces. In our analysis, we also introduce a different notion of area, namely the relaxation of the area w.r.t. a convergence stronger than the L^1 convergence, whose singular contribution is completely characterized in terms of suitable semicartesian area minimizing problems. We propose also some examples of maps for which the two notions of relaxation are different: these examples underline the highly non-local behaviour of the L^1-relaxation, and justify the introduction of the other functional. Some result about the existence of a semicartesian area-minimizing surface is also provided..
diritti: info:eu-repo/semantics/openAccess
In relazione con info:eu-repo/semantics/altIdentifier/hdl/20.500.11767/4846
Bellettini, Giovanni

Tesi di dottorato. | Lingua: Inglese. | Paese: | BID: TD17042596