论文标题
对分数最大分布函数和规律性理论应用的水平不平等现象
Level-set inequalities on fractional maximal distribution functions and applications to regularity theory
论文作者
论文摘要
本文的目的是建立基于所谓的最大最大分布函数（FMD）的抽象理论。从〜\ cite {AM2007}中介绍的粗略思想中，我们通过使用此类FMD的语言来开发并证明与级别的不平等和规范范围有关的一些抽象结果。特别有趣的是我们的方法的适用性已在规律性和calderón-Zygmund型估计中显示。在本文中，由于我们的研究经验，我们将通过分数 - 最大的操作员和FMD来建立两种类型的一般准线性问题（发散形式和双重障碍问题）的全球规律性估计。这些抽象结果的应用范围很大。除了讨论的椭圆方程式规则性理论的这两个示例外，也有望表明我们在其他特殊主题中进一步应用我们的方法。
The aim of this paper is to establish an abstract theory based on the so-called fractional-maximal distribution functions (FMDs). From the rough ideas introduced in~\cite{AM2007}, we develop and prove some abstract results related to the level-set inequalities and norm-comparisons by using the language of such FMDs. Particularly interesting is the applicability of our approach that has been shown in regularity and Calderón-Zygmund type estimates. In this paper, due to our research experience, we will establish global regularity estimates for two types of general quasilinear problems (problems with divergence form and double obstacles), via fractional-maximal operators and FMDs. The range of applications of these abstract results is large. Apart from these two examples of the regularity theory for elliptic equations discussed, it is also promising to indicate further possible applications of our approach for other special topics.
