On anisotropic Sobolev spaces
Hoai-Minh Nguyen, Marco Squassina
TL;DR
This paper explores new characterizations of anisotropic Sobolev and BV spaces, extending classical formulas to anisotropic and magnetic cases, providing deeper understanding of these function spaces.
Contribution
It introduces anisotropic versions of the Bourgain-Brezis-Mironescu formula, including for magnetic Sobolev and BV functions, advancing the theoretical framework.
Findings
Established anisotropic Bourgain-Brezis-Mironescu formulas
Extended formulas to magnetic Sobolev and BV spaces
Provided new characterizations for anisotropic function spaces
Abstract
We investigate two types of characterizations for anisotropic Sobolev and BV spaces. In particular, we establish anisotropic versions of the Bourgain-Brezis-Mironescu formula, including the magnetic case both for Sobolev and BV functions.
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