  In this paper, we study the differential inclusion associated to the minimal
surface system for two-dimensional graphs in $\mathbb{R}^{2 + n}$. We prove
regularity of $W^{1,2}$ solutions and a compactness result for approximate
solutions of this differential inclusion in $W^{1,p}$. Moreover, we make a
perturbation argument to infer that for every $R > 0$ there exists $\alpha(R)
>0$ such that $R$-Lipschitz stationary points for functionals $\alpha$-close in
the $C^2$ norm to the area functional are always regular. We also use a
counterexample of \cite{KIRK} to show the existence of irregular critical
points to inner variations of the area functional.
