A variational theory of the Hessian equation

Abstract

By studying a negative gradient flow of certain Hessian functionals we establish the existence of critical points of the functionals and consequently the existence of ground states to a class of nonhomogenous Hessian equations. To achieve this we derive uniform, first- and second-order a priori estimates for the elliptic and parabolic Hessian equations. Our results generalize well-known results for semilinear elliptic equations and the Monge-Ampère equation. Show more