Sobolev Embedding Theorem for Irregular Domains and Discontinuity of p -> p*(p,n)

Abstract

For a domain Ω we denote q as the supremum of all possible indices guaranteeing the embedding of the Sobolev space W^{1,p}(Ω) into the Lebesgue space L^q(Ω). We construct a domain Ω such that q is discontinuous.

Keywords

• Sobolev space
• Sobolev embedding