Backward Uniqueness for the Heat Equation in Cones

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Abstract

It was shown in [4, 14] that a bounded solution of the heat equation in a half-space which becomes zero at some time must be identically zero, even though no assumptions are made on the boundary values of the solutions. In a recent example, Luis Escauriaza showed that this statement fails if the half-space is replaced by cones with opening angle smaller than 90°. Here we show that the result remains true for cones with opening angle larger than 110°.

Original languageEnglish (US)
Pages (from-to)1414-1429
Number of pages16
JournalCommunications in Partial Differential Equations
Volume37
Issue number8
DOIs
StatePublished - Aug 2012

Bibliographical note

Funding Information:
L. L. is supported in part by Louise T. Dosdall fellowship and Doctoral Dissertation Fellowship. V. S. is supported in part by NSF grant DMS 0800908.

Keywords

  • Backward uniqueness
  • Cone domain
  • Heat equation
  • Parabolic equations

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