Compactness for Sobolev-type trace operators

Abstract

Compactness of arbitrary-order Sobolev type embeddings for traces of n-dimensional functions on lower dimensional subspaces is investigated. Sobolev spaces built upon any rearrangement-invariant norm are allowed.

In particular, we characterize compactness of trace embeddings for classical Sobolev, Lorentz-Sobolev and Orlicz- Sobolev type spaces. (C) 2019 Published by Elsevier Ltd.

Keywords

• Sobolev spaces
• Trace embeddings
• Optimal target
• Rearrangement-invariant spaces
• Lorentz spaces
• Orlicz spaces
• Supremum operators