Local solutions to a class of Monge-Ampère equations of mixed type

Abstract

In this article, we study a class of Monge-Ampère equations of mixed type which is elliptic in one side of a hypersurface and hyperbolic in another side. The degeneracy along the hypersurface is allowed to be at arbitrary, even infinite, order. The linearized equation is also of mixed type and includes the high-dimensional Tricomi equation as a special case. We establish the existence of sufficiently smooth local solutions to the Monge-Ampère equations via Nash-Moser iteration