Nonlocal characterizations of variable exponent Sobolev spaces

Article type: Research Article

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

Affiliations: Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via dei Musei 41, Brescia, Italy. E-mails: gianluca.ferrari03@icatt.it, marco.squassina@unicatt.it

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

Note: [**] The second 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 theory and in the theory of electrorheological fluids. We also get a singular limit formula extending Nguyen results to the anisotropic case.

Keywords: Anisotropic Sobolev spaces, singular limit formulas, nonlocal characterizations

DOI: 10.3233/ASY-211675

Journal: Asymptotic Analysis, vol. 127, no. 1-2, pp. 121-142, 2022