Carleman estimates for higher step Grushin operators
| Autor: | De Bie, Hendrik, Lian, Pan |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The higher step Grushin operators $\Delta_{\alpha}$ are a family of sub-elliptic operators which degenerate on a sub-manifold of $\mathbb{R}^{n+m}$. This paper establishes Carleman-type inequalities for these operators. It is achieved by deriving a weighted $L^{p}-L^{q}$ estimate for the Grushin-harmonic projector. The crucial ingredient in the proof is the addition formula for Gegenbauer polynomials due to T. Koornwinder and Y. Xu. As a consequence, we obtain the strong unique continuation property for the Schr\"odinger operators $-\Delta_{\alpha}+V$ at points of the degeneracy manifold, where $V$ belongs to certain $ L^{r}_{{\rm loc}}(\mathbb{R}^{n+m})$. Comment: Comments Welcome |
| Databáze: | arXiv |
| Externí odkaz: |
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