English

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 Γ\Gamma-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