A new proof of compactness in G(S)BD

Abstract

We prove a compactness result in GBD which also provides a new proof of the compactness theorem in GSBD, due to Chambolle and Crismale [5, Theorem 1.1]. Our proof is based on a Fréchet-Kolmogorov compactness criterion and does not rely on Korn or Poincaré-Korn inequalities.