论文标题
本质上lipchitz常数的固有cheeger能量
Intrinsic Cheeger energy for the intrinsically Lipschitz constants
论文作者
论文摘要
最近，在公制空间中，Le Donne和作者介绍了所谓的本质上Lipschitz部分。该注释的主要目的是在我们的新背景下适应古典Lipschitz常数的Cheeger理论。更准确地说，我们将固有的Cheeger Energy从$ l^2（y，\ r^s）$到$ [0，+\ infty]，$（y，d_y，\ mm）$是一个度量度量空间，我们以适当的放松坡度的概念来表征它。为了获得此结果，在更一般的环境中，我们建立了本质上Lipschitz常数的某些特性，例如Leibniz公式，产品公式和渐近性本质上Lipschitz常数的上半持续点。
Recently, in the metric spaces, Le Donne and the author introduced the so-called intrinsically Lipschitz sections. The main aim of this note is to adapt Cheeger theory for the classical Lipschitz constants in our new context. More precisely, we define the intrinsic Cheeger energy from $L^2(Y,\R^s)$ to $[0,+\infty],$ where $(Y,d_Y,\mm)$ is a metric measure space and we characterize it in terms of a suitable notion of relaxed slope. In order to get this result, in more general context, we establish some properties of the intrinsically Lipschitz constants like the Leibniz formula, the product formula and the upper semicontinuity of the asymptotic intrinsically Lipschitz constant.
