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

Autor:	Ahmed Aberqi, Omar Benslimane, Abdesslam Ouaziz, Dus̆an D. Repovs̆
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	Fractional p ( z ⋅ ) $p( z \cdot )$ -Laplacian Existence of solutions Fractional Sobolev space with variable exponent on complete manifolds Variational method Analysis QA299.6-433
Zdroj:	Boundary Value Problems, Vol 2022, Iss 1, Pp 1-20 (2022)
Druh dokumentu:	article
ISSN:	1687-2770
DOI:	10.1186/s13661-022-01590-5
Popis:	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 , ⋅ ) $p(z, \cdot )$ -Laplacian problems involving potentials with vanishing behavior at infinity as an application.
Databáze:	Directory of Open Access Journals
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