Uniformity of Maximal Hypoellipticity on Graded Lie Groups: From Pointwise to Global
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915674751762432 |
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| author | Liu, Shiqi McDonald, Edward Sukochev, Fedor Zanin, Dmitriy |
| author_facet | Liu, Shiqi McDonald, Edward Sukochev, Fedor Zanin, Dmitriy |
| contents | On graded Lie groups, we develop a mechanism that transfers the uniformity of maximal hypoellipcity from the frozen coefficients principal part of a differential operator to the full operator. Our approach brings the century-old "freeze-unfreeze" strategy into the hypoelliptic setting, and offers a transparent and flexible framework for lifting symbol-level hypoelliptic properties to global elliptic estimates, without relying on pseudodifferential calculus. In addition, we prove that symmetric operators of hypoelliptic type on a graded Lie group are self-adjoint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniformity of Maximal Hypoellipticity on Graded Lie Groups: From Pointwise to Global Liu, Shiqi McDonald, Edward Sukochev, Fedor Zanin, Dmitriy Analysis of PDEs Functional Analysis On graded Lie groups, we develop a mechanism that transfers the uniformity of maximal hypoellipcity from the frozen coefficients principal part of a differential operator to the full operator. Our approach brings the century-old "freeze-unfreeze" strategy into the hypoelliptic setting, and offers a transparent and flexible framework for lifting symbol-level hypoelliptic properties to global elliptic estimates, without relying on pseudodifferential calculus. In addition, we prove that symmetric operators of hypoelliptic type on a graded Lie group are self-adjoint. |
| title | Uniformity of Maximal Hypoellipticity on Graded Lie Groups: From Pointwise to Global |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2512.12646 |