Viscosity solutions of the Monge–Ampère equation with the right hand side in $L^p$

Abstract

In this paper we compare various notions of solutions of Monge–Ampère equations with discontinuous functions in the right hand side. Precisely, we show that the weak solutions defined by Trudinger can be obtained by the vanishing viscosity approximation method. Moreover, we investigate existence and uniqueness of $L^p$-viscosity solutions.