Moser-Trudinger type inequalities for the Hessian equation

摘要

The k-Hessian equation for k≥2 is a class of fully nonlinear partial differential equation of divergence form. A Sobolev type inequality for the k-Hessian equation was proved by the second author in 1994. In this paper, we prove the Moser-Trudinger type inequality for the k-Hessian equation.