Generalized Liouville theorem for viscosity solutions to a singular Monge-Ampère equation

Abstract

In this article, we study the asymptotic behaviour at infinity for viscosity solutions to a singular Monge-Ampère equation in half space from affine geometry. In particular, we extend the Liouville theorem for smooth solutions to the case of viscosity solutions by a completely different method from the smooth case.

Keywords

• liouville theorem
• asymptotic behaviour
• viscosity solution
• monge-ampère equation
• 35j96
• 35j60
• 35b40