An Extension Result for Generalised Special Functions of Bounded Deformation

We show an extension result for generalised special functions of bounded deformation (

, for every

p>1 p > 1

) and any dimension

n\geq 2 n ≥ 2

. The proof is based on a recent result of F. Cagnetti, A. Chambolle, and L. Scardia, showing that a function

u u

in

GSBD^p G S B D p

with a “small” jump set coincides with a

W^{1,p} W 1 , p

function, up to a small set whose perimeter and volume are controlled by the size of the jump of

u u

.