Compact embeddings of weighted variable exponent Sobolev spaces and existence of solutions for weighted p(•)-Laplacian

被引：10

作者：

Unal, Cihan ^{[1
]}

Aydin, Ismail ^{[2
]}

机构：

[1] Assessment Select & Placement Ctr, Ankara, Turkey

[2] Sinop Univ, Fac Arts & Sci, Dept Math, Sinop, Turkey

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2021年 / 66卷 / 10期

关键词：

Weak solution; compact embedding; p (center dot)-Laplacian; weighted variable exponent Sobolev spaces; GENERALIZED LEBESGUE; ELLIPTIC-EQUATIONS; DIRICHLET PROBLEM;

D O I：

10.1080/17476933.2020.1781831

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this study, we define double weighted variable exponent Sobolev spaces W-1,W-q(.),W-p(.) (Omega, theta(0),theta) with respect to two different weight functions. Also, we investigate the basic properties of this spaces. Moreover, we discuss the existence of weak solutions for weighted Dirichlet problem of p(center dot)-Laplacian equation -div(theta(x) vertical bar del f vertical bar p(x)(-2)del f) = theta(0)(x) vertical bar f vertical bar(q(x)-2) f x is an element of Omega f = 0 x is an element of partial derivative Omega under some conditions of compact embedding involving the double weighted variable exponent Sobolev spaces.

引用

页码：1755 / 1773

页数：19

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