Compact Trace In Weighted Variable Exponent Sobolev Spaces W^{1, P(x)}(Ω;v₀, V₁)

We study the trace operators in weighted variable exponent Sobolev spaces W^1,p(x)(Ω;v₀,v₁)→L^q(x)((?)Ω;w) for sufficiently regular unbounded domainΩ(?)R^N (N≥2) with noncompact boundary, where p(x) is a Lipschitz continuous function definedonΩsatisfying 1 < p^-≤p⁺< N. We show that when ess inf (N-1/q(x)-N/p(x)+1) > 0, the trace operators W^1,p(x)(Ω;v₀,v₁)→L^q(x)((?)Ω;w) is compact under certain conditionson weight functions v₀, v₁ w.