Moser–Trudinger type inequalities for the Hessian equation

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. © 2010 Elsevier Inc. All rights reserved