Holmgren’s Uniqueness Theorem

Marcelo R. Ebert and Michael Reissig
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Marcelo R. Ebert: University of São Paulo, Department of Computing and Mathematics
Michael Reissig: TU Bergakademie Freiberg, Institute of Applied Analysis

Chapter Chapter 5 in Methods for Partial Differential Equations, 2018, pp 49-55 from Springer

Abstract: 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.

Keywords: Uniqueness Assertion; Linear Cauchy Problem; Distributional Solutions; Classical Version; Abstract Version (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/978-3-319-66456-9_5

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