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Pré-Publication, Document De Travail Année : 2021

Propagation of singularities for subelliptic wave equations

Résumé

We revisit the paper [Mel86] by R. Melrose, providing a full proof of the main theorem on propagation of singularities for subelliptic wave equations, and linking this result with sub-Riemannian geometry. This result asserts that singularities of subelliptic wave equations only propagate along null-bicharacteristics and abnormal extremal lifts of singular curve. As a new consequence, for x = y and denoting by K G the wave kernel, we obtain that the singular support of the distribution t → K G (t, x, y) is included in the set of lengths of the normal geodesics joining x and y, at least up to the time equal to the minimal length of a singular curve joining x and y.
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Dates et versions

hal-03259054 , version 1 (14-06-2021)
hal-03259054 , version 2 (09-12-2021)
hal-03259054 , version 3 (07-05-2022)

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Citer

Cyril Letrouit. Propagation of singularities for subelliptic wave equations. 2021. ⟨hal-03259054v1⟩
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