Abstract
Our aim in this paper is to deal with Sobolev’s embeddings for Musielak–Orlicz–Sobolev functions in \(W^{1,\Phi }_0(\Omega )\) for \(\Omega \subset {\mathbb {R}}^N\), as extensions of Harjulehto and Hästö (Publ Mat 52:347–363, 2008), Hästö (Math Res Lett 16(2):263–278, 2009) and Hästö et al. (Glasg Math J 52:227–240, 2010). Here \(\Phi \) is a function such that \(\phi (x,t)=t^{-1} \Phi (x,t)\) is uniformly almost increasing positive function of \(t > 0\).
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Mizuta, Y., Ohno, T. & Shimomura, T. Sobolev inequalities for Musielak–Orlicz spaces. manuscripta math. 155, 209–227 (2018). https://doi.org/10.1007/s00229-017-0944-5
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DOI: https://doi.org/10.1007/s00229-017-0944-5