On critical \(\mathrm{L}^p\)-differentiability of BD-maps (Q2280522)

Summary: 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.