Optimality of function spaces in Sobolev embeddings

Abstract

We study optimality of function spaces that appear in Sobolev embeddings. We focus on rearrangement-invariant Banach function spaces.

Keywords

• Sobolev spaces
• rearrangement-invariant spaces
• optimal range
• optimal domain
• reduction theorems: compact embeddings
• fundamental functions
• traces
• Gaussian embeddings
• isoperimetric function