微分形式是现代微积分的基本工具之一,同时微分形式在现代微分几何、微分方程、群论及物理科学中有着非常广泛的应用。而A-调和方程是一种退化的椭圆方程。这个项目主要是研究关于变量是微分形式的非线性A-调和方程。研究内容主要包括关于它的解的存在性；在假设弱解存在的情况下，研究弱解的一些先验估计：Caccioppoli估计、弱逆Holder不等式以及弱解的Holder连续性等问题以及相关加权结果。

Differential form is one of the basic tools of modern calculus, at the same time differential form has been widely used in modern differential geometry, group theory, differential equations and physical science. And the A- harmonic equation is a degenerate elliptic equation. This project is mainly research on the variables are differential forms of a nonlinear A- harmonic equation. The research content mainly includes its existence of solution, some prior estimates of its weak solutions under the assumption of weak solutions existing, such as Caccioppoli estimates, reverse Holder inequality and the Holder continuity of the weak weak solutions and their related weighted results.