论文标题
最小图和差分夹杂物
Minimal graphs and differential inclusions
论文作者
论文摘要
在本文中，我们研究了$ \ mathbb {r}^{2 + n} $中二维图的最小表面系统相关的差分包含。我们证明了$ w^{1,2} $解决方案的规律性，并且对于在$ w^{1，p} $中近似解决方案的解决方案的紧凑性结果。此外，我们提出一个扰动论点，以推断出每一个$ r> 0 $都存在$α（r）> 0 $，以便$ r $ -lipschitz功能的固定点$α$ - 在该区域功能的$ c^2 $ norm中始终是常规的。我们还使用\ cite {kirk}的反例显示了面积功能的内部变化的不规则临界点。
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 $α(R) >0$ 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 \cite{KIRK} to show the existence of irregular critical points to inner variations of the area functional.
