Revista Matemática Iberoamericana

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

Sergio Polidoro and Maria Alessandra Ragusa

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We prove a Harnack inequality for the positive solutions of ultraparabolic equations of the type $$ \mathcal {L}_0 u + \mathcal {V} u = 0, $$ where $\mathcal {L}_0$ is a linear second order hypoelliptic operator and $\mathcal {V}$ 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.

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Rev. Mat. Iberoamericana, Volume 24, Number 3 (2008), 1011-1046.

First available in Project Euclid: 9 December 2008

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Primary: 35K70: Ultraparabolic equations, pseudoparabolic equations, etc. 35J10: Schrödinger operator [See also 35Pxx] 35K20: Initial-boundary value problems for second-order parabolic equations 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx] 35B65: Smoothness and regularity of solutions

hypoelliptic operator Schrödinger equation Harnack inequality Green function


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

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