4 papers
Gradient Estimates for Hessian Equations with Measure Data
Rongxun He
In this article, we establish the interior gradient estimates for -Hessian equations with measure data. We use the ideas from the potential theories for the -Laplacian type e…
On the Hessian Hardy-Sobolev Inequality and Related Variational Problems
Rongxun He, Wei Ke
In this paper, we first prove the Hardy-Sobolev inequality for the Hessian integral by means of a descent gradient flow of certain Hessian functionals. As an application, we study…
Weighted Eigenvalue Problem for a Class of Singular/Degenerate -Hessian Equations
Rongxun He, Genggeng Huang
In this paper, we study the existence and uniqueness of solutions to the weighted eigenvalue problem for -Hessian equation. To achieve this, we establish the uniform a priori es…
Uniqueness of positive solutions for finsler p-Laplacian equations with polynomial non-linearity
Rongxun He, Wei Ke
We consider the uniqueness of the following positive solutions of anisotropic elliptic equation: \begin{equation} \nonumber \left\{ \begin{aligned} -Δ^F_p u&=u^q \quad \text{in} \q…