Magnetic Fractional order Orlicz-Sobolev spaces
Analysis of PDEs
2018-12-17 v1
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 convergence of modulars and convergence of solutions for some non-local magnetic Laplacian allowing non-standard growth laws to its local counterpart.
Keywords
Cite
@article{arxiv.1812.05998,
title = {Magnetic Fractional order Orlicz-Sobolev spaces},
author = {Julián Fernández Bonder and Ariel Salort},
journal= {arXiv preprint arXiv:1812.05998},
year = {2018}
}
Comments
21 pages. arXiv admin note: text overlap with arXiv:1707.03267