Existence of optimizers in a Sobolev inequality for vector fields
Analysis of PDEs
2022-02-17 v2 Mathematical Physics
Classical Analysis and ODEs
Functional Analysis
math.MP
Abstract
We consider the minimization problem corresponding to a Sobolev inequality for vector fields and show that minimizing sequences are relatively compact up to the symmetries of the problem. In particular, there is a minimizer. An ingredient in our proof is a version of the Rellich--Kondrachov compactness theorem for sequences satisfying a nonlinear constraint.
Cite
@article{arxiv.2107.06450,
title = {Existence of optimizers in a Sobolev inequality for vector fields},
author = {Rupert L. Frank and Michael Loss},
journal= {arXiv preprint arXiv:2107.06450},
year = {2022}
}
Comments
31 pages. This is the publication version, incorporating the journal style