Tealdi, LuciaBellettini, GiovanniPaolini, Maurizio2015-08-102015-08-102015-08-07https://openscience.sissa.it/handle/1963/34488The article is compsed of 18 pages and is recorded in PDF formatWe 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'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.enDirichlet energyarea-minimizing surfacessemicartesian surfacesPreprintMAT/05