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An Extension Result for Generalised Special Functions of Bounded Deformation

Cagnetti, Filippo; Chambolle, Antonin; Perugini, Matteo; Scardia, Lucia (2020), An Extension Result for Generalised Special Functions of Bounded Deformation, Journal of Convex Analysis, 28, 2, p. 457-470

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Journal of Convex Analysis
Volume
28
Number
2
Publisher
Heldermann
Pages
457-470
Metadata
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Author(s)
Cagnetti, Filippo
Department of Mathematics [Sussex]
Chambolle, Antonin cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Perugini, Matteo
Westfälische Wilhelms-Universität Münster = University of Münster [WWU]
Scardia, Lucia
School of Mathematical and Computer Sciences [MATHEMATICS DEPARTMENT OF HERIOT-WATT UNIVERSITY]
Abstract (EN)
We show an extension result for functions in GSBD^p , for every p > 1 and any dimension n ≥ 2. The proof is based on a recent result in [9], where it is shown that a function u in GSBD^p with a "small" jump set coincides with a W^{1,p} function, up to a small set whose perimeter and volume are controlled by the size of the jump of u.
Subjects / Keywords
Free-discontinuity problems; functions of bounded deformation; Griffith's energy