Concentration effects of BV gradients have gradient structure

TL;DR

This paper proves that concentration effects from weakly-* convergent BV gradient sequences have an inherent gradient structure, contrasting with oscillation phenomena, thus advancing understanding of BV map behaviors.

Contribution

The paper establishes a rigorous link between concentration effects and gradient structure in BV maps, providing new insights into their convergence properties.

Findings

Concentration effects exhibit a gradient structure in BV maps.

Contrasts with oscillation phenomena in BV sequences.

Provides a theoretical foundation for analyzing BV gradient convergence.

Abstract

We prove that the concentration effects arising from weakly-* convergent sequences of gradients of maps of bounded variation have gradient structure. This is in stark contrast with the corresponding oscillation phenomena.