  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.
