Hörmander's theorem for parabolic equations with coefficients measurable in the time variable

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Abstract

We are dealing with possibly degenerate second-order parabolic operators whose coefficients are infinitely differentiable with respect to the space variables and only measurable with respect to the time variable. We impose the Hörmander condition on the diffusion coefficients and prove that the solutions of the corresponding equations with right-hand sides which are infinitely differentiable in the space variables in a space-time domain also have this property.

Original languageEnglish (US)
Pages (from-to)854-870
Number of pages17
JournalSIAM Journal on Mathematical Analysis
Volume46
Issue number1
DOIs
StatePublished - 2014

Keywords

  • Hypoellipticity
  • Measurable coefficients
  • Parabolic operators

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