Optimal regularity for codimension one minimal surfaces with a free boundary.
Optimal Regularity Theorems for Variational Problems with Obstacles.
Optimal segmentation of unbounded functions
Optimal transportation for the determinant
Among -valued triples of random vectors (X,Y,Z) having fixed marginal probability laws, what is the best way to jointly draw (X,Y,Z) in such a way that the simplex generated by (X,Y,Z) has maximal average volume? Motivated by this simple question, we study optimal transportation problems with several marginals when the objective function is the determinant or its absolute value.
Optimality conditions and exact solutions of the two-dimensional Monge-Kantorovich problem.
Optimality conditions for nonconvex variational problems relaxed in terms of Young measures
The scalar nonconvex variational problems of the minimum-energy type on Sobolev spaces are studied. As the Euler–Lagrange equation dramatically looses selectivity when extended in terms of the Young measures, the correct optimality conditions are sought by means of the convex compactification theory. It turns out that these conditions basically combine one part from the Euler–Lagrange equation with one part from the Weierstrass condition.