The sharp affine $L^2$ Sobolev trace inequality and variants
Functional Analysis
2025-03-14 v2 Analysis of PDEs
Abstract
We establish a sharp affine Sobolev trace inequality by using the Busemann-Petty centroid inequality. For , our affine version is stronger than the famous sharp Sobolev trace inequality proved independently by Escobar and Beckner. Our approach allows also to characterize all cases of equality in this case. For this new inequality, no Euclidean geometric structure is needed.
Cite
@article{arxiv.1512.04621,
title = {The sharp affine $L^2$ Sobolev trace inequality and variants},
author = {Pablo Luis De Nápoli and Julián Haddad and Carlos Hugo Jiménez and Marcos Montenegro},
journal= {arXiv preprint arXiv:1512.04621},
year = {2025}
}
Comments
17 pages including an appendix. The main results from the previous version remain unchanged. The structure and notations were modified, several typos were corrected and proofs for some technical lemmas were added