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. Andrea Braides and Margherita Solci are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni-Istituto Nazionale di Alta Matematica.
Discrete approximation of nonlocal-gradient energies / Braides, Andrea; Causin, Andrea; Solci, Margherita. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8266. - 17:4(2024), pp. 1507-1518. [10.1515/acv-2023-0028]
Discrete approximation of nonlocal-gradient energies
Andrea Braides;Andrea Causin;Margherita Solci
2024-01-01
Abstract
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. Andrea Braides and Margherita Solci are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni-Istituto Nazionale di Alta Matematica.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
