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

Agnid Banerjee; Nicola Garofalo; Ramesh Manna

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

Analysis of PDEs 2019-10-01 v2

Authors: Agnid Banerjee , Nicola Garofalo , Ramesh Manna

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.

Keywords

carleman estimates baouendi-grushin operators quantitative unique continuation strong unique continuation degenerate equations

Cite

@article{arxiv.1903.08382,
  title  = {Carleman estimates for Baouendi-Grushin operators with applications to quantitative uniqueness and strong unique continuation},
  author = {Agnid Banerjee and Nicola Garofalo and Ramesh Manna},
  journal= {arXiv preprint arXiv:1903.08382},
  year   = {2019}
}

Comments

revised version of the file, several references have been added

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