We present inversion results for Lipschitz maps f : Ω ⊂ ℝN → (Y, d) and stability of inversion for uniformly convergent sequences. These results are based on the Area Formula and on the l.s.c. of metric Jacobians.
We provide an approximation of Mather variational problem by finite dimensional minimization problems in the framework of -convergence. By a linear programming interpretation as done in [Evans and Gomes, ESAIM: COCV (2002) 693–702] we state a duality theorem for the Mather problem, as well a finite dimensional approximation for the dual problem.
By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds to a...
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