Continuity for the Monge mass transfer problem in two dimensions (Q1710408)

The authors investigate the continuity of the monotone optimal mapping of the (more than two centuries old) Monge mass transfer problem in two dimensions under some hypotheses imposed on the domains and the mass distributions. The strict separation assumptions previously considered in the literature are no longer necessary in this new approach that makes use of the so-called \(\mathcal{D}\)-curves.