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Strictly Hyperbolic Operators and Approximate Energies

  • Ferruccio Colombini
  • Daniele Del Santo
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 10)

Abstract

In this note we collect some results on Sobolev-, CO- and Gevrey-well-posedness of the Cauchy problem for linear strictly hyperbolic operators having non Lipschitz-continuous coefficients. These results are obtained modifying the classical method of the energy estimates by the introduction of the so-called approximate energies, i.e. a family of energies which depend on a small parameter.

Keywords

Cauchy Problem Energy Estimate Hyperbolic Case Linear Partial Differential Operator Nonlinear Hyperbolic Equation 
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© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Ferruccio Colombini
    • 1
  • Daniele Del Santo
    • 2
  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly
  2. 2.Dipartimento di Scienze MatematicheUniversità di TriesteTriesteItaly

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