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arXiv · 2106.06954

A Bourgain-Brezis-Mironescu representation for functions with bounded deformation

Adolfo Arroyo-Rabasa·Paolo Bonicatto
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Abstract

We establish a non-local integral difference quotient representation for symmetric gradient semi-norms in $BD(Ω)$ and $LD(Ω)$, which does not require the manipulation of distributional derivatives. Our representation extends the formulas for the symmetric gradient established by Mengesha for vector-fields in $W^{1,p}(Ω;\mathbb R^d)$, which are inspired by the gradient semi-norm formulas introduced by Bourgain, Brezis and Mironescu in $W^{1,p}(Ω)$ and by Dávila in $BV(Ω)$.

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Adolfo Arroyo-Rabasa, Paolo Bonicatto. 2021-06-29. A Bourgain-Brezis-Mironescu representation for functions with bounded deformation. https://arxiv.org/abs/2106.06954

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