We establish a non-local integral difference quotient representation for symmetric gradient semi-norms in BD(Omega) and LD(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,W-p (Omega; R-d), which are inspired by the gradient semi-norm formulas introduced by Bourgain, Brezis and Mironescu in W-1,W-p (Omega) and by Davila in BV (Omega).
A Bourgain-Brezis-Mironescu representation for functions with bounded deformation
Arroyo-Rabasa, Adolfo;
2023-01-01
Abstract
We establish a non-local integral difference quotient representation for symmetric gradient semi-norms in BD(Omega) and LD(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,W-p (Omega; R-d), which are inspired by the gradient semi-norm formulas introduced by Bourgain, Brezis and Mironescu in W-1,W-p (Omega) and by Davila in BV (Omega).File in questo prodotto:
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