Minimal graphs and differential inclusions

2020/02/06 by Tione, Riccardo · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.02157

Abstract

In this paper, we study the differential inclusion associated to the minimal surface system for two-dimensional graphs in 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 α(R) >0 such that R-Lipschitz stationary points for functionals α-close in the C² norm to the area functional are always regular. We also use a counterexample of \citeKIRK to show the existence of irregular critical points to inner variations of the area functional.

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