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Abstract
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We prove space-time dispersive estimates for solutions to the wave equation on compact
Riemannian manifolds with bounded curvature tensor, where we assume that the metric tensor
is of
regularity
for some
,
which ensures that the curvature tensor is well-defined in the weak sense. The
estimates are established for the same range of Lebesgue and Sobolev exponents that
hold in the case of smooth metrics. Our results are for bounded time intervals, so by
finite propagation velocity they hold also on noncompact manifolds under
appropriate uniform geometry conditions.
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Keywords
wave equation, dispersive estimates
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Mathematical Subject Classification 2010
Primary: 58J45
Secondary: 35L15
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Milestones
Received: 8 August 2018
Revised: 12 September 2018
Accepted: 22 October 2018
Published: 21 November 2018
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