Magnetic fractional order Orlicz–Sobolev spaces
Tom 259 / 2021
Studia Mathematica 259 (2021), 1-24 MSC: 46E30, 35R11, 45G05. DOI: 10.4064/sm190713-5-7 Opublikowany online: 10 December 2020
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 $\varGamma $-convergence of modulars and convergence of solutions for some nonlocal magnetic Laplacian allowing nonstandard growth laws to its local counterpart.