Minimal graphs and differential inclusions
Minimal graphs and differential inclusions
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DOI：
10.1080/03605302.2020.1871367
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发表时间：
2021-01-07
影响因子：
1.9
通讯作者：
Tione, Riccardo
中科院分区：
文献类型：
--
作者：
Tione, Riccardo
本文研究了R ~ 2 +n中二维图的极小曲面系统的微分包含：证明了W-1，W- 2解的正则性，并给出了该微分包含在W-1，W- p中的近似解的紧性结果：此外，我们做了一个微扰的论点来推断，对于每一个R> 0，存在α（R）> 0使得在C-2范数下a-接近面积泛函的R-Lipschitz驻点总是正则的.我们还使用了B的一个反例。Kirchhem（2003）证明了面积泛函内部变化的不规则临界点的存在。
In this paper, we study the differential inclusion associated with the minimal surface system for two-dimensional graphs in R2+n: We prove regularity of W-1,W- 2 solutions and a compactness result for approximate solutions of this differential inclusion in W-1,W- 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 a-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.