Compact embeddings for Sobolev spaces of two variable exponents

We study the compact embedding for Sobolev spaces W-0(1,phi)(G) of two variable exponents, where Phi(x, t) = t(p(x))(log(e + t))(q(x)). Here p(.) and q(.) are variable exponents satisfying the log-Holder and log log-Holder conditions, respectively.

Automated summary

The study focuses on the compact embedding properties of Sobolev spaces with two variable exponents, where the exponents satisfy certain conditions.