Compact embeddings of weighted variable exponent Sobolev spaces and existence of solutions for weighted <i>p</i> (·)-Laplacian
Compact embeddings of weighted variable exponent Sobolev spaces and existence of solutions for weighted <i>p</i> (·)-Laplacian
In this study, we define double weighted variable exponent Sobolev spaces W1,q(⋅),p(⋅)Ω,ϑ0,ϑ 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(⋅)-Laplacian equation −divϑ(x)∇fp(x)−2∇f=ϑ0(x)fq(x)−2fx∈Ωf=0x∈∂Ω under some conditions of compact embedding …