KMS Inequalities: From Elliptic Operators to Constant Rank
Abstract
Korn-Maxwell-Sobolev (KMS) inequalities represent a tool for estimating differential expressions and have gained particular importance in recent years, especially concerning elliptic operators. In my Master's thesis, together with Peter Lewintan (University of Duisburg-Essen), we extended this concept to also apply to operators of constant rank. This makes it possible to cover more complex structures such as the curl or divergence of vector fields. A key difference from the elliptic theory is that in the constant rank case, a correction term is necessary on the left-hand side of the inequality. Results were also obtained for the limiting case , although additional assumptions are required here. This article provides an illustrative introduction to KMS inequalities and demonstrates their application in both the elliptic and constant rank cases.
Keywords
Cite
@article{arxiv.2504.00798,
title = {KMS Inequalities: From Elliptic Operators to Constant Rank},
author = {Paul Stephan},
journal= {arXiv preprint arXiv:2504.00798},
year = {2025}
}
Comments
English version preprint of an invited article originally published in German by De Gruyter in 'Mitteilungen der Deutschen Mathematiker-Vereinigung'. The final published version can be found at https://doi.org/10.1515/dmvm-2025-0011