# Carleman estimates for Baouendi-Grushin operators with applications to quantitative uniqueness and strong unique continuation

## TL;DR

This paper develops new Carleman estimates for Baouendi-Grushin operators and applies them to extend quantitative unique continuation results and establish strong unique continuation for certain degenerate equations.

## Contribution

The paper introduces novel $L^{2}-L^{2}$ Carleman estimates for Baouendi-Grushin operators and applies these to advance unique continuation properties.

## Key findings

- Extended Bourgain-Kenig quantitative unique continuation.
- Proved strong unique continuation for degenerate sublinear equations.
- Established new Carleman estimates for degenerate operators.

## Abstract

In this paper we establish some new $L^{2}-L^{2}$ Carleman estimates for the Baouendi-Grushin operators $\mathscr{B}_\gamma$, in (1.1) below. We apply such estimates to obtain: (i) an extension of the Bourgain-Kenig quantitative unique continuation; (ii) the strong unique continuation property for some degenerate sublinear equations.