Nonlocal characterizations of variable exponent Sobolev spaces

TL;DR

This paper develops nonlocal characterizations for variable exponent Sobolev spaces, extending existing results to anisotropic cases and applications in nonlinear elasticity and electrorheological fluids.

Contribution

It introduces new nonlocal characterization methods for variable exponent Sobolev spaces, including a singular limit formula for anisotropic cases, expanding theoretical understanding.

Findings

Extended Nguyen's singular limit results to anisotropic Sobolev spaces

Provided nonlocal characterizations relevant to nonlinear elasticity

Connected Sobolev space theory with applications in electrorheological fluids

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.