An Extension Result for Generalised Special Functions of Bounded Deformation

We show an extension result for generalised special functions of bounded deformation (GSBD(p), for every p > 1) and any dimension n >= 2. The proof is based on a recent result of F. Cagnetti, A. Chambolle, and L. Scardia, where it is shown that a function u in GSBD(p) with a small jump set coincides with a W-1,W-p function, up to a small set whose perimeter and volume are controlled by the size of the jump of u.

Automated summary

This study provides an extension result for generalised special functions of bounded deformation and shows that a function in GSBD(p) with a small jump set coincides with a W-1,W-p function, up to a small set whose perimeter and volume are controlled by the size of the jump of the function.