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

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.

7 pages; to appear in Rev. Mat. Iberoam

Cited by in corpus (1)

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