Nonlocal approximations to anisotropic Sobolev norms

Article type: Research Article

Authors: Cinelli, Ivan | Ferrari, Gianluca | Squassina, Marco^{; **; *}

Affiliations: Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via della Garzetta 48, Brescia, Italy. E-mails: ivan.cinelli01@icatt.it, gianluca.ferrari03@icatt.it, marco.squassina@unicatt.it

Correspondence: [*] Corresponding author. E-mail: marco.squassina@unicatt.it.

Note: [**] The third author is member of Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

Abstract: We obtain some nonlocal characterizations for a class of variable exponent Sobolev spaces arising in nonlinear elasticity, in the theory of electrorheological fluids as well as in image processing for the regions where the variable exponent p(x) reaches the value 1.

Keywords: Anisotropic Sobolev spaces, nonlocal characterizations, image processing

DOI: 10.3233/ASY-211749

Journal: Asymptotic Analysis, vol. 130, no. 1-2, pp. 213-232, 2022