On critical $mathrm{L}^p$-differentiability of $mathrm{BD}$-maps

We prove that functions of locally bounded deformation on $mathbb{R}^n$ are $mathrm{L}^{n/(n-1)}$-differentiable 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, linear differential operator $mathbb{A}$ has finite dimensional null-space.