Abstract
In this paper, we study the differential inclusion associated with the minimal surface system for two-dimensional graphs in We prove regularity of solutions and a compactness result for approximate solutions of this differential inclusion in Moreover, we make a perturbation argument to infer that for every R > 0, there exists such that R-Lipschitz stationary points for functionals α-close in the C 2 norm to the area functional are always regular. We also use a counterexample of B. Kirchhem (2003) to show the existence of irregular critical points to inner variations of the area functional.
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