Published Paper

Inserted: 15 jun 2026
Last Updated: 15 jun 2026

Journal: Nonlinear Analysis
Year: 2025
Doi: https://doi.org/10.1016/j.na.2024.113683

Abstract:

We introduce a general difference quotient representation for non-local operators associated with a first-order linear operator. We establish new local to non-local estimates and strong localization principles in various spaces of functions, measures and distributions, which fully generalize those known for gradients. Under suitable assumptions, we also establish the invariance of quasiconvexity within the proposed local-nonlocal setting. Applications to the fine properties of $\mathcal A$-gradient measures are further discussed.

Tags: ConFine