@mastersthesis {2015,
	title = {The relaxed area of maps from the plane to the plane with a line discontinuity, and the role of semicartesian surfaces.},
	year = {2015},
	school = {SISSA},
	abstract = {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.},
	keywords = {Area functional},
	author = {Lucia Tealdi}
}
@article {2015,
	title = {Results on the minimization of the Dirichlet functional among semicartesian parametrizations},
	year = {2015},
	note = {The article is compsed of 18 pages and is recorded in PDF format},
	abstract = {<p>We start to investigate the existence of conformal minimizers for the Dirichlet functional in the setting of the so-called semicartesian parametrizations, adapting to this context some techniques used in solving the classical Plateau{\textquoteright}s problem. The final goal is to find area minimizing semicartesian parametrizations spanning a Jordan curve obtained as union of two graphs; this problem appeared in the study of the relaxed area functional for maps from the plane to the plane jumping on a line.</p>},
	url = {http://urania.sissa.it/xmlui/handle/1963/34488},
	author = {Lucia Tealdi and Giovanni Bellettini and Maurizio Paolini}
}
