We prove a Harnack inequality for the positive solutions of ultraparabolic equations of the type L u + V u = 0;where L is a linear second order hypoelliptic differential operator and 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.
Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term / Polidoro, Sergio; Ragusa, M. A.. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - STAMPA. - 24:3(2008), pp. 1011-1046. [10.4171/RMI/565]
Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term
POLIDORO, Sergio;
2008
Abstract
We prove a Harnack inequality for the positive solutions of ultraparabolic equations of the type L u + V u = 0;where L is a linear second order hypoelliptic differential operator and 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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