A general compactness theorem in $G(S)BD$

TL;DR

This paper presents a simplified proof of a compactness theorem in the space of generalized special functions of bounded deformation, applicable to both $GSBD^p$ and $GBD$, demonstrating convergence after removing piecewise rigid motions.

Contribution

The authors provide a new, more straightforward proof of a compactness result in $GSBD^p$ and $GBD$, extending previous results and simplifying the convergence analysis.

Findings

Bounded sequences converge almost everywhere after removing piecewise infinitesimal rigid motions.

The compactness result applies to both $GSBD^p$ for $p>1$ and $GBD$ for $p=1$.

The proof is simpler than previous approaches, facilitating further research.

Abstract

We give a new, simpler proof of a compactness result in $GSBD^p$, $p>1$, by the same authors, which is also valid in $GBD$ (the case $p=1$), and shows that bounded sequences converge a.e., after removal of a suitable sequence of piecewise infinitesimal rigid motions, subject to a fixed partition.