Magnetic fractional order orlicz-sobolev spaces

Abstract

We define the notion of nonlocal magnetic Sobolev spaces with nonstandard 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 Γ-convergence of modulars and convergence of solutions for some nonlocal magnetic Laplacian allowing nonstandard growth laws to its local counterpart.