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 < p− p+ < N. We show that when ess infx∈Ω ( N−1 q(x) − N p(x) +1) > 0, the trace operators W1,p(x)(Ω; v0, v1) → Lq(x)(∂Ω; w) are compact under certain conditions on weight functions v0, v1, w.