| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 88 | |
| Number of page(s) | 21 | |
| DOI | https://doi.org/10.1051/cocv/2025073 | |
| Published online | 05 November 2025 | |
Domains of dependence for subelliptic wave equations and unique continuation for fractional powers of Hörmander’s operators
1
Université Paris-Saclay, Laboratoire de Mathématique d’Orsay, UMR 8628 du CNRS 91405 Orsay Cedex, France
2
Institut universitaire de France, France
* Corresponding author: nicolas.burq@universite-paris-saclay.fr
Received:
16
September
2024
Accepted:
29
August
2025
We prove the sharp domain of dependence property for solutions to subelliptic wave equations for sums of squares of vector fields satisfying Hörmander bracket condition. We deduce a unique continuation property for the square root of subelliptic Laplace operators under an additional analyticity condition. Then, with a different, more involved method, we prove the same result of unique continuation for more general s-powers (0 < s < 1).
Mathematics Subject Classification: 35A02 / 35H20 / 35L05
Key words: Subelliptic / waves / domain of dependence / unique continuation
© The authors. Published by EDP Sciences, SMAI 2025
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