Area functional and relaxation: an approach in dimension 2 and codimension 2 via strict BV-convergence

In this thesis we address the problem of relaxation of the Cartesian area functional with respect to the strict convergence in $BV$ for maps $u:\Om\subset\R^2\to\R^2$. The relaxation technique allows to extend the notion of non-parametric area of $C^1$-maps to more general, possibly singular, maps. Explicit integral formulae are provided for the relaxed area of relevant classes of singular maps.