Compact trace in weighted variable exponent Sobolev spaces W1,p(x)(Ω;v0,v1)

We study trace operators in weighted variable exponent Sobolev spaces W1,p(x)(Ω;v0,v1)↪Lq(x)(∂Ω;w) for sufficiently regular unbounded domain Ω⊆RN (N⩾2) with noncompact boundary, where p(x) is a Lipschitz continuous function defined on Ω satisfying 1