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H Well-Posedness for Degenerate p-Evolution Models of Higher Order with Time-Dependent Coefficients

  • Torsten HerrmannEmail author
  • Michael Reissig
  • Karen Yagdjian
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 44)

Abstract

In this paper we deal with time dependent p-evolution Cauchy problems. The differential operators have characteristics of variable multiplicity. We consider a degeneracy only in t=0. We shall prove a well-posedness result in the scale of Sobolev spaces using a C 1-approach. In this way we will prove H well-posedness with an (at most) finite loss of regularity.

Keywords

p-Evolution equations Well-posedness Loss of derivatives Oscillations in coefficients Schrödinger type operators 

Mathematics Subject Classification

35J10 35Q41 

Notes

Acknowledgements

The joint considerations were supported by the German Research Foundation (DFG) in project GZ: RE 961/18-1.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Torsten Herrmann
    • 1
    Email author
  • Michael Reissig
    • 1
  • Karen Yagdjian
    • 2
  1. 1.Faculty of Mathematics and Computer ScienceTU Bergakademie FreibergFreibergGermany
  2. 2.Department of MathematicsUniversity of Texas—Pan AmericanEdinburgUSA

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