On critical $L^p$-differentiability of BD-maps

Abstract

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