Characterizations of anisotropic high order Sobolev spaces

Article type: Research Article

Authors: Lam, Nguyen^a | Maalaoui, Ali^b | Pinamonti, Andrea^{c; *}

Affiliations: [a] Department of Mathematics and The Pacific Institute for the Mathematical Sciences, University of British Columbia, Vancouver, BC V6T1Z4, Canada. E-mail: nlam@math.ubc.ca | [b] Department of Mathematics and Natural Sciences, American University of Ras Al Khaimah, PO Box 10021, Ras Al Khaimah, UAE. E-mail: ali.maalaoui@aurak.ac.ae | [c] Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38123 Povo, Trento, Italy. E-mail: andrea.pinamonti@unitn.it

Correspondence: [*] Corresponding author. E-mail: andrea.pinamonti@unitn.it.

Abstract: We establish two types of characterizations for high order anisotropic Sobolev spaces. In particular, we prove high order anisotropic versions of Bourgain–Brezis–Mironescu’s formula and Nguyen’s formula.

Keywords: High order Sobolev spaces, asymptotic characterization, anisotropic Sobolev spaces

DOI: 10.3233/ASY-181515

Journal: Asymptotic Analysis, vol. 113, no. 4, pp. 239-260, 2019