Galkowski, J;
Zworski, M;
(2021)
Analytic hypoellipticity of Keldysh operators.
Proceedings of the London Mathematical Society
10.1112/plms.12405.
(In press).
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Abstract
We consider Keldysh-type operators, P = x1D2 x1 + a(x)Dx1 + Q(x, Dx ), x = (x1, x ) with analytic coefficients, and with Q(x, Dx ) second order, principally real and elliptic in Dx for x near zero. We show that if P u = f, u ∈ C∞, and f is analytic in a neighbourhood of 0, then u is analytic in a neighbourhood of 0. This is a consequence of a microlocal result valid for operators of any order with Lagrangian radial sets. Our result proves a generalized version of a conjecture made in (Lebeau and Zworski, Proc. Amer. Math. Soc. 147 (2019) 145–152; Zworski, Bull. Math. Sci. 7 (2017) 1–85) and has applications to scattering theory.
| Type: | Article |
|---|---|
| Title: | Analytic hypoellipticity of Keldysh operators |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1112/plms.12405 |
| Publisher version: | https://doi.org/10.1112/plms.12405 |
| Language: | English |
| Additional information: | © 2021 The Authors. Proceedings of the London Mathematical Society is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | 35B65, 35H10 (primary), 35Q75, 58J47 (secondary) |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10124993 |
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