A Gradient Type Term for the k-Hessian Equation.

In this paper, we propose a gradient type term for the k-Hessian equation that extends for k > 1 the classical quadratic gradient term associated with the Laplace equation. We prove that such as gradient term is invariant by the Kazdan–Kramer change of variables. As applications, we ensure the existence of solutions for a new class of k-Hessian equation in the sublinear and superlinear cases for Sobolev type growth. The threshold for existence is obtained in some particular cases. In addition, for the Trudinger–Moser type growth regime, we also prove the existence of solutions under either subcritical or critical conditions. [ABSTRACT FROM AUTHOR]