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Harnack inequality for a class of Kolmogorov–Fokker–Planck equations in non-divergence form

  • Farhan Abedin
  • Giulio TralliEmail author
Article
  • 16 Downloads

Abstract

We prove invariant Harnack inequalities for certain classes of non-divergence form equations of Kolmogorov type. The operators we consider exhibit invariance properties with respect to a homogeneous Lie group structure. The coefficient matrix is assumed either to satisfy a Cordes–Landis condition on the eigenvalues, or to admit a uniform modulus of continuity.

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Notes

Acknowledgements

F.A. wishes to thank Prof. Brian Rider for providing financial support through his NSF Grant DMS–1406107. G.T. has been partially supported by the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The authors would like to thank Prof. Luis Silvestre for suggesting this problem at the 2017 Chicago Summer School in Analysis, and the anonymous referee for their valuable comments on the manuscript.

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Conflict of interest

The authors declare that they have no conflict of interest.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA
  2. 2.Dipartimento d’Ingegneria Civile e Ambientale (DICEA)Università di PadovaPadovaItaly

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