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Articles

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

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Pages 3667-3688 | Received 08 Oct 2019, Accepted 28 Dec 2019, Published online: 29 Jan 2020
 

ABSTRACT

In this paper, we establish some new L2L2 Carleman estimates for the Baouendi–Grushin operators Bγ, in Equation (1). We apply such estimates to obtain: (i) an extension of the Bourgain–Kenig quantitative unique continuation and (ii) the strong unique continuation property for some degenerate sublinear equations.

2010 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

First author is supported by SERB Matrix grant MTR/2018/000267. Second author is supported in part by a Progetto SID (Investimento Strategico di Dipartimento) ‘Non-local operators in geometry and in free boundary problems, and their connection with the applied sciences’, University of Padova, 2017. Third author is supported by SERB National Postdoctoral fellowship, PDF/2017/002780.

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