Sharp energy estimats for a class of weakly hyperbolic operators
M. Dreher and I. Witt
Abstract.
The intention of this article is twofold: First, we survey our results from
Dreher/Witt (2002)
and
Dreher/Witt (2005)
about energy estimates for the Cauchy problem for weakly hyperbolic
operators with finite time degeneracy at time t=0.
Then, in a second part, we show that these energy estimates are sharp
for a wide range of examples. In particular, for these examples we
precisely determine the loss of regularity that occurs in passing from
the Cauchy data at $t=0$ to the solutions.
New Trends in the Theory of Hyperbolic Equations,
Oper. Theory Adv. Appl.
159
(2005),
449-511.
The paper is available here:
pdf.
