Abstract

We show an extension result for generalised special functions of bounded deformation (GSBDpGSBD^p, for every p>1p>1) and any dimension n≥2n\geq 2. The proof is based on a recent result of F. Cagnetti, A. Chambolle, and L. Scardia, showing that a function uu in GSBDpGSBD^p with a ``small'' jump set coincides with a W1,pW^{1,p} function, up to a small set whose perimeter and volume are controlled by the size of the jump of uu.

Author information

Contact details are reproduced from the original publication and may be historical.

Lucia Scardia

Department of Mathematics, Heriot-Watt University, Edinburgh, United Kingdom

l.scardia@hw.ac.uk

Keywords

  • Free-discontinuity problems
  • functions of bounded deformation
  • Griffith's energy

Mathematics Subject Classification

49Q20, 70G75, 74R10

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Suggested citation

F. Cagnetti, A. Chambolle, M. Perugini, L. Scardia. “An Extension Result for Generalised Special Functions of Bounded Deformation.” Journal of Convex Analysis 28 (2021), No. 2, 457–470. https://doi.org/10.68381/jca28026

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press LLC.