JournalsrmiVol. 24, No. 3pp. 1011–1046

Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term

  • Sergio Polidoro

    Università di Bologna, Italy
  • Maria Alessandra Ragusa

    Università degli Studi di Catania, Italy
Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term cover
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Abstract

We prove a Harnack inequality for the positive solutions of ultraparabolic equations of the type

L0u+Vu=0,\mathcal {L}_0 u + \mathcal {V} u = 0,

where L0\mathcal {L}_0 is a linear second order hypoelliptic operator and V\mathcal {V} belongs to a class of functions of Stummel-Kato type. We also obtain the existence of a Green function and an uniqueness result for the Cauchy-Dirichlet problem.

Cite this article

Sergio Polidoro, Maria Alessandra Ragusa, Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term. Rev. Mat. Iberoam. 24 (2008), no. 3, pp. 1011–1046

DOI 10.4171/RMI/565