Some results of capacity in fractional Sobolev spaces with variable exponents

被引：0

作者：

Akdim, Youssef ^{[1
]}

Elharch, Rachid ^{[2
]}

Hassib, M. C. ^{[2
]}

Rhali, Soumia Lalaoui ^{[2
]}

机构：

[1] Univ Sidi Mohamed Ben Abdellah, Fac Sci Dhar El Mahraz, Dept Math, LAMA Lab, Atlas Fez 1796, Morocco

[2] Sidi Mohamed Ben Abdellah Univ, Polydisciplinary Fac Taza, Lab Engn Sci LSI, Taza 1223, Morocco

来源：

JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS | 2023年 / 9卷 / 01期

关键词：

Fractional Sobolev spaces with variable exponents; Capacity; Fractional Sobolev spaces and zero boundary values; Dirichlet energy; ZERO BOUNDARY-VALUES; LEBESGUE;

D O I：

10.1007/s41808-022-00189-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this note is to study the theory of capacity in fractional Sobolev spaces with variable exponents. We focus on the most important properties of this capacity including the convergence of a sequence, the determination of subsets of S1 with null capacity. In addition, we define the fractional Sobolev space with variable exponents and zero boundary values and we prove some of its basic properties, such as reflexivity. To illustrate our results, we show that the Dirichlet energy has a minimizer in fractional Sobolev spaces with variable exponents.

引用

页码：93 / 106

页数：14

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