KMS Inequalities: From Elliptic Operators to Constant Rank
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908294096879616 |
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| author | Stephan, Paul |
| author_facet | Stephan, Paul |
| contents | 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 $Π_\mathbb{B}$ is necessary on the left-hand side of the inequality. Results were also obtained for the limiting case $p=1$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_00798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | KMS Inequalities: From Elliptic Operators to Constant Rank Stephan, Paul Analysis of PDEs 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 $Π_\mathbb{B}$ is necessary on the left-hand side of the inequality. Results were also obtained for the limiting case $p=1$, 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. |
| title | KMS Inequalities: From Elliptic Operators to Constant Rank |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.00798 |