On a new fractional Sobolev space with variable exponent on complete manifolds

Ahmed Aberqi (Author), Omar Benslimane (Author), Abdesslam Ouaziz (Author), Dušan Repovš (Author)

Abstract

We present the theory of a new fractional Sobolev space in complete manifolds with variable exponent. As a result, we investigate some of our new space’s qualitative properties, such as completeness, reflexivity, separability, and density. We also show that continuous and compact embedding results are valid. We apply the conclusions of this study to the variational analysis of a class of fractional ▫$p(z, \cdot)$▫-Laplacian problems involving potentials with vanishing behavior at infinity as an application.

Keywords

fractional ▫$p(z, \cdot)$▫-Laplacian;existence of solutions;fractional Sobolev space with variable exponent on complete manifolds;variational method;

Data

Language:	English
Year of publishing:	2022
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	517.956
COBISS:	96892419
ISSN:	1687-2770
Views:	336
Downloads:	87
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	art. 7 (20 str.)
Issue:	ǂVol. ǂ2022
Chronology:	2022
DOI:	10.1186/s13661-022-01590-5
ID:	14673450