Minimum principles and a priori estimates for 2-Hessian problems
Abstract
In this paper we investigate a class of -Hessian equations and establish a minimum principle for a -function in the sense of L.E. Payne (see R. Sperb \cite{Sp81}). The analysis is based on a sharp matrix inequality providing an estimate for a suitable combination of second-order partial derivatives of the solution. Exploiting this estimate, we derive a differential inequality for the associated -function and obtain a minimum principle in higher dimensions under a convexity assumption. As an application of our results, together with convexity results established in X.-N. Ma and L. Xu \cite{MX08}, P. Liu, X.-N. Ma and L. Xu \cite{LMX10}, P. Salani \cite{Sa12}, and Y. Ye \cite{Ye13}, we derive a priori bounds for solutions of several classical -Hessian boundary value problems.
Cite
@article{arxiv.2603.19740,
title = {Minimum principles and a priori estimates for 2-Hessian problems},
author = {Cristian Enache},
journal= {arXiv preprint arXiv:2603.19740},
year = {2026}
}