  This paper is interested in the description of the density of particles
evolving according to some optimal policy of an impulse control problem. We
first fix sets on which the particles jump and explain how we can characterize
such a density. We then investigate the coupled case in which the underlying
impulse control problem depends on the density we are looking for : the mean
field games of impulse control. In both cases, we give a variational
characterization of the densities of jumping particles.

Analysis of PDEs