An Extension Result for Generalised Special Functions of Bounded Deformation
Filippo Cagnetti, Antonin Chambolle, Matteo Perugini, Lucia Scardia · Journal of convex analysis · 2021
We show an extension result for generalised special functions of bounded deformation ( GSBD^p G S B D p , 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 .