The aim of this paper is to prove the existence of minimizers for a variational problem
involving the minimization under volume constraint of the sum of the perimeter and a non …

This paper deals with a variant of the optimal transportation problem. Given f∈ L 1 (R d,[0,
1]) and a cost function c∈ C (R d× R d) of the form c (x, y)= k (yx), we minimise∫ cd γ among …

Consider the class of zero-mean functions with fixed L∞ and L 1 norms and exactly N∈ N
nodal points. Which functions f minimize W p (f+, f-), the Wasserstein distance between the …

We characterize the maximizers of a functional that involves the minimization of the
Wasserstein distance between sets of equal volume. We prove that balls are the only …

Chapter 2 is dedicated to the exterior transport term. In a general framework, we show that
the variational problem defining it has solutions and a dual formulation. Using stronger …