Dirichlet型边界条件下分式$p（x）$-Laplace问题的弱解

IF 0.2 Q4 MATHEMATICS

Methods of Functional Analysis and Topology Pub Date : 2020-09-28 DOI:10.31392/mfat-npu26_3.2020.08

Abdelali Sabri, A. Jamea, H. Alaoui

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引用次数: 0

摘要

在本文中，我们证明了一类具有Dirichlet型边界条件的分数p（x）-拉普拉斯问题的弱解的存在性和唯一性结果，这里使用的主要工具是与具有变量指数的分数Sobolev空间理论相结合的变分法。“我®¤®£® A“áã§÷§”®“我®美分̈p（x）——̉«»至÷®§£至®岛®美分®岛到岛®美分¥® ¥®在¥¬̄a® 在®£® 至®§aã。A®在®美分到÷æ÷©̈© ¥®？÷¥®到÷ï®“我®美分̈å̄至®a®至÷®“我®¥§÷®£® ̄®在Aã。

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Weak solution for fractional $p(x)$-Laplacian problem with Dirichlet-type boundary condition

In the present paper, we prove the existence and uniqueness result of weak solutions to a class of fractional p(x)-Laplacian problem with Dirichlet-type boundary condition, the main tool used here is the varitional method combined with the theory of fractional Sobolev spaces with variable exponent. «ï ®¤®£® a« áã § ¤ ç ÷§ ¤à®¡®¢ ̈¬ p(x)-« ̄« á÷ ®¬ § £à ̈ç®î ã¬®¢®î â ̈ ̄ã ̈à ̈å«¥ ¤®¢¥¤¥® â¥®à¥¬ã ̄à® ÷áã¢ ï â õ¤ ̈÷áâì á« ¡a®£® à®§¢'ï§aã. ̈a®à ̈áâ®¢ãîâìáï ¢ à÷ æ÷© ̈© ¬¥â®¤ ÷ â¥®à÷ï ¤à®¡®¢ ̈å ̄à®áâ®à÷¢ ®¡®«¥¢ §¬÷®£® ̄®àï¤aã.

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来源期刊

Methods of Functional Analysis and Topology MATHEMATICS-

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： Methods of Functional Analysis and Topology (MFAT), founded in 1995, is a peer-reviewed arXiv overlay journal publishing original articles and surveys on general methods and techniques of functional analysis and topology with a special emphasis on applications to modern mathematical physics.