Communications in Partial Differential Equations ( IF 2.1 ) Pub Date : 2021-02-03 , DOI: 10.1080/03605302.2020.1871367 Riccardo Tione 1
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 C2 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.
中文翻译:
最小图形和微分包含
摘要
在本文中,我们研究了与二维图的最小表面系统相关的微分包含 我们证明的规律性 解和这种微分包含的近似解的紧致性结果 此外,我们提出了一个扰动论证来推断,对于每一个R > 0,存在使得泛函α 的R -Lipschitz 驻点在C 2范数中接近区域泛函总是规则的。我们还使用 B. Kirchhem (2003) 的反例来展示区域函数内部变化的不规则临界点的存在。