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

被引：12

作者：

Aberqi, Ahmed ^{[1
]}

Benslimane, Omar ^{[2
]}

Ouaziz, Abdesslam ^{[2
]}

Repovs, Dusan D. ^{[3
]}

机构：

[1] Sidi Mohamed Ben Abdellah Univ, Nat Sch Appl Sci, Fes, Morocco

[2] Sidi Mohamed Ben Abdellah Univ, Fac Sci Dhar el Mahraz, Fes, Morocco

[3] Univ Ljubljana, Fac Math & Phys, Jadranska 19, SI-1000 Ljubljana, Slovenia

来源：

BOUNDARY VALUE PROBLEMS | 2022年 / 2022卷 / 01期

关键词：

Fractional p(z; )-Laplacian; Existence of solutions; Fractional Sobolev space with variable exponent on complete manifolds; Variational method; FUNCTIONALS; EQUATIONS; THEOREMS;

D O I：

10.1186/s13661-022-01590-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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, .)-Laplacian problems involving potentials with vanishing behavior at infinity as an application.

引用

页数：20

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