Compact embedding theorems and a Lions' type Lemma for fractional Orlicz-Sobolev spaces
Analysis of PDEs
2020-10-21 v1
Abstract
In this paper we are concerned with some abstract results regarding to fractional Orlicz-Sobolev spaces. Precisely, we ensure the compactness embedding for the weighted fractional Orlicz-Sobolev space into the Orlicz spaces, provided the weight is unbounded. We also obtain a version of Lions' "vanishing" Lemma for fractional Orlicz-Sobolev spaces, by introducing new techniques to overcome the lack of a suitable interpolation law. Finally, as a product of the abstract results, we use a minimization method over the Nehari manifold to prove the existence of ground state solutions for a class of nonlinear Schr\"{o}dinger equations, taking into account unbounded or bounded potentials.
Keywords
Cite
@article{arxiv.2010.10277,
title = {Compact embedding theorems and a Lions' type Lemma for fractional Orlicz-Sobolev spaces},
author = {Edcarlos D. Silva and Marcos L. M. Carvalho and José Carlos de Albuquerque and Sabri Bahrouni},
journal= {arXiv preprint arXiv:2010.10277},
year = {2020}
}