Lipschitz estimates for partial trace operators with extremal Hessian eigenvalues

Abstract We consider the Dirichlet problem for partial trace operators which include smallest and largest eigenvalue of Hessian matrix. It is related to two-player zero-sum differential games. No Lipschitz regularity result known solutions, our knowledge. If some missing, such are nonlinear, degenerate, non-uniformly elliptic, neither convex nor concave. Here we prove an interior estimate under a non-standard assumption: that solution exists in larger, unbounded domain, vanishes at infinity. In other words, need condition coming from far away. also provide existence results showing this satisfied large class solutions. On occasion, extend few qualitative properties uniformly elliptic operators, operators.