Existence results for Isaacs equations with local conditions and related semilinear Cauchy problems

Our goal is to prove existence results for classical solutions to some general nondegenerate Cauchy problems which are natural generalizations of Isaacs equations. For the latter we are able to extend our results by admitting local conditions for coefficients. Such equations appear naturally for instance in robust control theory. Using our general results, we can solve not only Isaacs equations, but also equations for other sophisticated control problems, for instance models with state dependent constraints on the control set.