Calculus of Variations and Geometric Measure Theory

A. Braides - A. Causin - M. Solci

Discrete approximation of nonlocal-gradient energies

created by braidesa on 21 Jun 2023
modified on 10 Dec 2023


Published Paper

Inserted: 21 jun 2023
Last Updated: 10 dec 2023

Journal: Adv. Calc. Var.
Year: 2023
Doi: 10.1515/acv-2023-0028

ArXiv: 2303.00842 PDF


We study a discrete approximation of functionals depending on nonlocal gradients. The discretized functionals are proved to be coercive in classical Sobolev spaces. The key ingredient in the proof is a formulation in terms of circulant Toeplitz matrices.

Keywords: Nonlocal Gradients, discrete-to-continuum, Discrete approximation, Toeplitz matrices