Viscosity solutions of the augmented K-Hessian equations in exterior domains

Abstract

This paper examines the Dirichlet problem for augmented -Hessian equations in exterior domains. Building upon our previous results on the viscosity solutions to the Dirichlet problems for augmented -Hessian equations in the bounded domain, and L. Dai, J. Bao's method to the -Hessian equations in exterior domains, a sufficient condition for the existence and uniqueness of viscosity solutions to the Dirichlet problem for the augmented -Hessian equations in exterior domains have been proven. During the process, a slight adjustment to the result on the existence and uniqueness of viscosity solutions to the problem in the bounded domains has been made for use in the present situation.