Calculus of Variations and Geometric Measure Theory

S. Almi - E. Tasso

A new proof of compactness in G(S)BD

created by tasso on 28 Apr 2021
modified on 14 Jan 2022


Published Paper

Inserted: 28 apr 2021
Last Updated: 14 jan 2022

Journal: Advances in Calculus of Variations
Year: 2022
Doi: 10.1515/acv-2021-0041

ArXiv: 2104.13141 PDF


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.