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Holmgren’s Uniqueness Theorem

In: Methods for Partial Differential Equations

Author

Listed:
  • Marcelo R. Ebert

    (University of São Paulo, Department of Computing and Mathematics)

  • Michael Reissig

    (TU Bergakademie Freiberg, Institute of Applied Analysis)

Abstract

Holmgren’s uniqueness theorem is one of the fundamental results in the theory of partial differential equations. It is related to the Cauchy-Kovalevskaja theorem. Theorem 4.1.1 implies a uniqueness result in the class of analytic solutions to a large class of Cauchy problems for partial differential equations. This uniqueness assertion still allows for the possibility that there may exist other classical or even distributional solutions which are not necessarily analytic. The classical theorem of Holmgren states that this can not happen in the set of classical solutions. As in Chapter 4 , we explain the classical version and the abstract version in scales of Banach spaces as well.

Suggested Citation

  • Marcelo R. Ebert & Michael Reissig, 2018. "Holmgren’s Uniqueness Theorem," Springer Books, in: Methods for Partial Differential Equations, chapter 0, pages 49-55, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-66456-9_5
    DOI: 10.1007/978-3-319-66456-9_5
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