P. A Bourgain–Brezis–Mironescu representation for functions with bounded deformation

Arroyo Rabasa, Adolfo;Bonicatto, P.
(2022) Calculus of Variations, Classical and Modern — Vol. 62, n° 1, p. 1-22 (2022)

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Authors
  • Arroyo Rabasa, AdolfoUCLouvain
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  • Bonicatto, P.
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Abstract
We establish a non-local integral difference quotient representation for symmetric gradient semi-norms in $B D(\Omega)$ and $L D(\Omega)$, 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 $W^{1,p}(\Omega; \mathbb{R}^d)$, which are inspired by the gradient seminorm formulas introduced by Bourgain, Brezis and Mironescu in $W^{1,p}(\Omega)$ and by Dávila in $BV(\Omega)$.
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Arroyo Rabasa, A., & Bonicatto, P. (2022). P. A Bourgain–Brezis–Mironescu representation for functions with bounded deformation. Calculus of Variations, Classical and Modern, 62(1), 1-22. https://hdl.handle.net/2078.5/103068 (Original work published 2022)