Viscosity solutions of the Monge-Ampère equation with the right hand side in \(L^p\)
Summary: 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 \textit{N. S. Trudinger} [Commun. Partial Differ. Equations 22, No. 7--8, 1251--1261 (1997; Zbl 0883.35035)] can be obtained by the vanishing viscosity approximation method. Moreover, we investigate existence and uniqueness of \(L^p\)-viscosity solutions.
scientific article; zbMATH DE number 5292678