Revista Matemática Iberoamericana

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Volume 35, Issue 7, 2019, pp. 2071–2078
DOI: 10.4171/rmi/1111

Published online: 2019-07-17

On critical $L^p$-differentiability of BD-maps

Franz Gmeineder[1] and Bogdan Raiță[2]

(1) Universität Bonn, Germany
(2) University of Warwick, Coventry, UK

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.

Keywords: Approximate differentiability, convolution operators, functions with bounded variation, functions with bounded deformation

Gmeineder Franz, Raiță Bogdan: On critical $L^p$-differentiability of BD-maps. Rev. Mat. Iberoam. 35 (2019), 2071-2078. doi: 10.4171/rmi/1111