Can I read Carleman estimates for higher step Grushin operators on EtoBox?

Carleman estimates for higher step Grushin operators by De Bie, Hendrik; Lian, Pan is a scholarly article available to read on EtoBox.

What is Carleman estimates for higher step Grushin operators about?

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})$.

Author

De Bie, Hendrik; Lian, Pan

Published

2024

Language

EN