A gradient type term for the $k$-Hessian equation
Analysis of PDEs
2024-04-01 v1
Abstract
In this paper, we propose a gradient type term for the -Hessian equation that extends for 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 -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.
Cite
@article{arxiv.2301.07201,
title = {A gradient type term for the $k$-Hessian equation},
author = {Mykael de Araújo Cardoso and Jefferson de Brito Sousa and José Francisco de Oliveira},
journal= {arXiv preprint arXiv:2301.07201},
year = {2024}
}