Nichtlineare partielle Differentialgleichungen vom gemischten elliptisch-hyperbolischen Typ

Abstract

This thesis studies the article "Local solutions to a class of Monge-Ampère equations of mixed type" by Qing Han (Duke Math. J., Vol. 136, No. 3, 2007). The article proves the existence of sufficiently smooth local solutions for a special kind of Monge-Ampère equations, which change their type monotonically across a hypersurface from elliptic to hyperbolic resp. vice versa, where the order of degeneracy may be infinite. We elaborate Han's proof via Nash-Moser iterations for solutions of the linearized equations, which are degenerately elliptic resp. hyperbolic, fill some gaps und correct a few inaccuracies.