Functional and variational aspects of nonlocal operators associated with linear PDEs (Q6650541)

A general framework for representing non-local operators associated with a first-order linear operator is introduced using a difference quotient approach. New estimates bridging local and non-local behaviors are derived, and robust localization principles across various functional, measure, and distribution spaces are established, extending results previously known for gradients. The preservation of quasiconvexity in this local-nonlocal context is demonstrated under appropriate conditions. Additionally, applications to the fine structural properties of \(\mathcal{A}\)-gradient measures are explored.