Gevrey regularity of subelliptic Monge–Ampère equations in the plane

In this paper, we establish the Gevrey regularity of solutions for a class of degenerate Monge–Ampère equations in the plane. Under the assumptions that one principal entry of the Hessian is strictly positive and the coefficient of the equation is degenerate with appropriately finite type degeneracy, we prove that the solution of the degenerate Monge–Ampère equation will be smooth in Gevrey classes.