论文标题
在Orlicz-Sobolev-Slobodeckij和有限变化空间中，张量字段，广义钟形多项式的高阶链条规则和估计值
Higher-order chain rules for tensor fields, generalized Bell polynomials, and estimates in Orlicz-Sobolev-Slobodeckij and bounded variation spaces
论文作者
论文摘要
我们描述了多元功能和张量场的高阶链条规则。我们估计张变量变化后张量场较高衍生物的较高衍生物的较高衍生物的总变异符号，并确定坐标变化的足够规律条件。我们还为多元函数的组成链引入了一种新颖的高阶链条规则，该规则通过嵌套集和广义的铃铛多项式描述。它是FaàdiBruno公式的自然扩展。我们的讨论使用张量计算的无坐标语言，并包括Banach空间之间的Fréchet不同映射。
We describe higher-order chain rules for multivariate functions and tensor fields. We estimate Sobolev-Slobodeckij norms, Musielak-Orlicz norms, and the total variation seminorms of the higher derivatives of tensor fields after a change of variables and determine sufficient regularity conditions for the coordinate change. We also introduce a novel higher-order chain rule for composition chains of multivariate functions that is described via nested set partitions and generalized Bell polynomials; it is a natural extension of the Faà di Bruno formula. Our discussion uses the coordinate-free language of tensor calculus and includes Fréchet-differentiable mappings between Banach spaces.
