Germ hypoellipticity and loss of derivatives
| Autor: | Gregorio Chinni |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Proceedings of the American Mathematical Society. 140:2417-2427 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/s0002-9939-2011-11252-8 |
| Popis: | We prove hypoellipticity in the sense of germs for the operator \[ P = L q L ¯ q + L ¯ q t 2 k L q + Q 2 , \mathcal {P}= L_{q}\overline {L}_{q} + \overline {L}_{q}t^{2k}L_{q} +Q^{2}, \] where \[ L q = D t + i t q − 1 − Δ x and Q = x 1 D 2 − x 2 D 1 , L_{q}=D_{t}+it^{q-1}\sqrt {-\Delta _{x}}\quad \text {and}\quad Q = x_{1}D_{2}-x_{2}D_{1}, \] even though it fails to be hypoelliptic in the strong sense. The primary tool is an a priori estimate. |
| Databáze: | OpenAIRE |
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