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This paper demonstrates unique continuation for subelliptic Laplacians and explores domains of dependence in solutions, indicating implications for mathematical physics.
We prove the sharp domain of dependence property for solutions to subelliptic wave equa- tions 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).
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Burq et al. (2025) studied this question.
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