  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.
