Yuxuan Liao

Existence of classical solutions to the exterior Dirichlet problem for Hessian quotient equations

This paper studies the exterior Dirichlet problem for Hessian quotient equations with nonconstant right-hand sides. We prove the existence of classical admissible solutions with prescribed asymptotic Hessians and establish convergence of the Hessian at infinity. The main difficulties are obtaining second-order estimate...