A new proof of compactness in G(S)BD

TL;DR

This paper presents a novel proof of a compactness theorem in GSBD, utilizing a Fréchet-Kolmogorov criterion, offering an alternative to traditional inequality-based methods.

Contribution

It introduces a new proof technique for compactness in GBD and GSBD that avoids Korn and Poincaré-Korn inequalities, simplifying the theoretical framework.

Findings

Provides a new proof of the compactness theorem in GSBD

Uses Fréchet-Kolmogorov criterion instead of inequalities

Simplifies understanding of compactness in GBD and GSBD

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 Fr\'echet-Kolmogorov compactness criterion and does not rely on Korn or Poincar\'e-Korn inequalities.