| I will present a joint work with Favre and Jonsson, whose goal is to solve the non-Archimedean analogue of Monge-Ampere equations on certain Berkovich spaces by using a variational approach. In order to do so, we develop some aspects of pluripotential theory in this non-Archimedean situation, and prove among other things a regularization and a weak compactness theorem for psh functions. |