Abstract
AbstractIn this paper we consider the wave equations for hypoelliptic homogeneous left-invariant operators on graded Lie groups with time-dependent Hölder (or more regular) non-negative propagation speeds. The examples are the time-dependent wave equation for the sub-Laplacian on the Heisenberg group or on general stratified Lie groups, or $p$
p
-evolution equations for higher order operators on ${{\mathbb{R}}}^{n}$
R
n
or on groups, already in all these cases our results being new. We establish sharp well-posedness results in the spirit of the classical result by Colombini, De Giorgi and Spagnolo. In particular, we describe an interesting local loss of regularity phenomenon depending on the step of the group (for stratified groups) and on the order of the considered operator.
Funder
Engineering and Physical Sciences Research Council
Leverhulme Trust
Fonds Wetenschappelijk Onderzoek
Publisher
Springer Science and Business Media LLC
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