JournalsrmiVol. 35, No. 7pp. 2071–2078

On critical LpL^p-differentiability of BD-maps

  • Franz Gmeineder

    Universität Bonn, Germany
  • Bogdan Raiță

    University of Warwick, Coventry, UK
On critical $L^p$-differentiability of BD-maps cover
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Abstract

We prove that functions of locally bounded deformation on Rn\mathbb{R}^n are Ln/(n1)\mathrm{L}^{{n}/{(n-1)}}-differentiable Ln\mathcal{L}^n-almost everywhere. More generally, we show that this critical Lp\mathrm{L}^p-differentiability result holds for functions of locally bounded A\mathbb{A}-variation, provided that the first order, homogeneous differential operator A\mathbb{A} has finite dimensional null-space.

Cite this article

Franz Gmeineder, Bogdan Raiță, On critical LpL^p-differentiability of BD-maps. Rev. Mat. Iberoam. 35 (2019), no. 7, pp. 2071–2078

DOI 10.4171/RMI/1111