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Sharp Energy Estimates for a Class of Weakly Hyperbolic Operators

  • Michael Dreher
  • Ingo Witt
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 159)

Abstract

The intention of this article is twofold: First, we survey our results from [20, 18] 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.

Keywords

Weakly hyperbolic operators finite time degeneracy well-posedness of the Cauchy problem sharp energy estimates loss of regularity 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Michael Dreher
    • 1
  • Ingo Witt
    • 2
  1. 1.Fachbereich Mathematik und StatistikUniversität KonstanzKonstanzGermany
  2. 2.Institut für MathematikUniversität PotsdamPotsdamGermany

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