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Contributions to the optimal transport problem and its regularity

Prod'homme, Maxime

This thesis deals with the optimal transport problem, in particular with regularity properties shared by optimal transport maps. The first part of this manuscript provides a new proof of the Caffarelli contraction theorem, stating that the optimal transport map from the gaussian measure to a measure with a uniformly log-concave density with respect...

Some contributions to geometric variational problems involving nonlocal energies

Pegon, Marc

This thesis is dedicated to the study of two separate geometric variational problems involving nonlocal energies: firstly, the geometry and singularities of fractional harmonic maps,and secondly, an iso perimetric problem with a repulsive integrable potential inspired by Gamow’s liquid drop model for the atomic nucleus. On the first topic, we impro...

Publication search with Régularité partielle as keyword

Contributions to the optimal transport problem and its regularity

Some contributions to geometric variational problems involving nonlocal energies

Publication search
with Régularité partielle as keyword