Continuity points via Riesz potentials for $\mathbb{C}$-elliptic operators

TL;DR

This paper introduces a Riesz potential criterion to identify Lebesgue continuity points for functions of bounded -variation associated with -elliptic differential operators, extending classical results.

Contribution

It provides a new criterion based on Riesz potentials for continuity points in the context of -variation functions involving -elliptic operators of any order.

Findings

Established a Riesz potential criterion for -variation functions.

Extended classical continuity results to -elliptic operators.

Potential applications to classical functions of bounded variation.

Abstract

We establish a Riesz potential criterion for Lebesgue continuity points of functions of bounded $\mathbb{A}$-variation, where $\mathbb{A}$ is a $\mathbb{C}$-elliptic differential operator of arbitrary order. This result might even be of interest for classical functions of bounded variation.