Banerjee, A and Manna, R (2021) Carleman estimates for a class of variable coefficient degenerate elliptic operators with applications to unique continuation. In: Discrete and Continuous Dynamical Systems- Series A, 41 (11). pp. 5105-5139.
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Abstract
In this paper, we obtain new Carleman estimates for a class of variable coefficient degenerate elliptic operators whose constant coefficient model at one point is the so called Baouendi-Grushin operator. This generalizes the results obtained by the two of us with Garofalo in 10 where similar estimates were established for the "constant coefficient" Baouendi-Grushin operator. Consequently, we obtain: (i) a Bourgain-Kenig type quantitative uniqueness result in the variable coefficient setting; (ii) and a strong unique continuation property for a class of degenerate sublinear equations. We also derive a subelliptic version of a scaling critical Carleman estimate proven by Regbaoui in the Euclidean setting using which we deduce a new unique continuation result in the case of scaling critical Hardy type potentials. © 2021 American Institute of Mathematical Sciences. All rights reserved.
| Item Type: | Journal Article |
|---|---|
| Publication: | Discrete and Continuous Dynamical Systems- Series A |
| Publisher: | American Institute of Mathematical Sciences |
| Additional Information: | The copyright for this article belongs to Author |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 02 Dec 2021 12:29 |
| Last Modified: | 02 Dec 2021 12:29 |
| URI: | http://eprints.iisc.ac.in/id/eprint/70061 |
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