In this talk, we consider an Isaacs equation and study the regularity
of solutions in Sobolev and Holder spaces. This class of equations
arises in the study of two-players, zero-sum, stochastic di erential games.
In addition, it is a toy-model for non-convex/non-concave operators. In
the framework of viscosity solutions, fundamental developments regarding
the Isaacs equation have been produced; for example, the existence and
uniqueness of solutions. We propose an approximation method, relating
the Isaacs operator with a Bellman one. From a heuristic viewpoint, we
import regularity from the latter to our problem of interest, by imposing
a proximity regime. Distinct regimes yield di erent classes of estimates,
covering the cases of Sobolev and Holder spaces. We close the talk with
some consequences and applications of our results.
