# Magnetic Fractional order Orlicz-Sobolev spaces

## TL;DR

This paper introduces nonlocal magnetic Orlicz-Sobolev spaces with non-standard growth, establishes a Bourgain-Brezis-Mironescu type formula, and explores convergence properties of non-local magnetic Laplacians.

## Contribution

It defines new nonlocal magnetic Sobolev spaces with non-standard growth and proves fundamental formulas and convergence results for these spaces.

## Key findings

- Bourgain-Brezis-Mironescu type formula established
- Gamma-convergence of modulars demonstrated
- Convergence of solutions for non-local magnetic Laplacians shown

## Abstract

In this paper we define the notion of nonlocal magnetic Sobolev spaces with non-standard growth for Lipschitz magnetic fields. In this context we prove a Bourgain - Brezis - Mironescu type formula for functions in this space as well as for sequences of functions. Finally, we deduce some consequences such as the $\Gamma-$convergence of modulars and convergence of solutions for some non-local magnetic Laplacian allowing non-standard growth laws to its local counterpart.