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 W1,p(Ω ; Rd) , which are inspired by the gradient semi-norm formulas introduced by Bourgain, Brezis and Mironescu in W1,p(Ω) and by Dávila in BV(Ω).
A Bourgain–Brezis–Mironescu representation for functions with bounded deformation / Arroyo-Rabasa, Adolfo; Bonicatto, Paolo. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 62:1(2023), pp. 3301-3322. [10.1007/s00526-022-02350-0]
A Bourgain–Brezis–Mironescu representation for functions with bounded deformation
Bonicatto, Paolo
2023-01-01
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 W1,p(Ω ; Rd) , which are inspired by the gradient semi-norm formulas introduced by Bourgain, Brezis and Mironescu in W1,p(Ω) and by Dávila in BV(Ω).| File | Dimensione | Formato | |
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