Journal of Convex Analysis 28 (2021), No. 2, 457--470
Copyright Heldermann Verlag 2021
An Extension Result for Generalised Special Functions of Bounded Deformation
Filippo Cagnetti
Department of Mathematics, University of Sussex, Brighton, United Kingdom
f.cagnetti@sussex.ac.uk
Antonin Chambolle
CMAP -- CNRS, Ecole Polytechnique, Palaiseau, France
antonin.chambolle@cmap.polytechnique.fr
Matteo Perugini
Institut für numerische und angewandte Mathematik, Westf.-Wilhelms-Universität, Münster, Germany
matteo.perugini@uni-muenster.de
Lucia Scardia
Department of Mathematics, Heriot-Watt University, Edinburgh, United Kingdom
l.scardia@hw.ac.uk
[Abstract-pdf]
We show an extension result for generalised special functions of bounded deformation ($GSBD^p$, for every $p>1$) and any dimension $n\geq 2$. The proof is based on a recent result of F.\,Cagnetti, A.\,Chambolle, and L.\,Scardia, showing 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 $u$.
Keywords: Free-discontinuity problems, functions of bounded deformation, Griffith's energy.
MSC: 49Q20, 70G75, 74R10.
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