On critical Lp-differentiability of BD-maps

被引：10
|
作者：
Gmeineder, Franz [1 ]
Rai, Bogdan [2 ]
机构：
[1] Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany
[2] Univ Warwick, Math Inst, Zeeman Bldg, Coventry CV4 7HP, W Midlands, England
来源：
REVISTA MATEMATICA IBEROAMERICANA | 2019年 / 35卷 / 07期
基金：
英国工程与自然科学研究理事会;
关键词：
Approximate differentiability; convolution operators; functions with bounded variation; functions with bounded deformation; INEQUALITY;
D O I：
10.4171/RMI/1111
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that functions of locally bounded deformation on R-n are Ln/(n-1)-differentiable L-n-almost everywhere. More generally, we show that this critical L-p-differentiability result holds for functions of locally bounded A-variation, provided that the first order, homogeneous differential operator A has finite dimensional null-space.
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页码：2071 / 2078
页数：8
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