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arXiv · 1802.10364

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

Franz Gmeineder·Bogdan Raita
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Abstract

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.

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Franz Gmeineder, Bogdan Raita. 2018-02-28. On critical $\mathrm{L}^p$-differentiability of $\mathrm{BD}$-maps. https://doi.org/10.4171/rmi%2F1111

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