Global Compactness, subcritical approximation of the Sobolev quotient, and a related concentration result in the Heisenberg group

TL;DR

This paper explores the effects of non-compactness in the critical Sobolev embedding within the Heisenberg group, focusing on compactness issues, subcritical approximations, and concentration phenomena.

Contribution

It introduces new insights into the behavior of Sobolev embeddings in the Heisenberg group, including subcritical approximation techniques and concentration results.

Findings

Identification of lack of compactness effects in the Sobolev embedding

Development of subcritical approximation methods

Establishment of concentration phenomena in the Heisenberg group

Abstract

We investigate some effects of the lack of compactness in the critical Sobolev embedding in the Heisenberg group.