Existence of extremal functions in higher-order affine Sobolev inequalities
Functional Analysis
2026-04-02 v1
Abstract
In this article, we prove the existence of extremal functions in higher-order affine Sobolev inequalities. Proofs rely on concentration-compactness methods in spaces of integer or fractional regularity. The tools we use, available in spaces of arbitrary regularity, might be of independent interest.
Keywords
Cite
@article{arxiv.2604.00640,
title = {Existence of extremal functions in higher-order affine Sobolev inequalities},
author = {Tristan Bullion-Gauthier},
journal= {arXiv preprint arXiv:2604.00640},
year = {2026}
}