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arXiv · 2309.05992

Domains of dependence for subelliptic wave equations and unique continuation for fractional powers of H\"ormander's operators

Nicolas Burq·Claude Zuily
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Abstract

We prove the sharp domain of dependence property for solutions to subelliptic wave equations for sums of squares of vector fields satisfying H\"ormander 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 ($0<s<1$).

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Nicolas Burq, Claude Zuily. 2023-09-12. Domains of dependence for subelliptic wave equations and unique continuation for fractional powers of H\"ormander's operators. https://arxiv.org/abs/2309.05992

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