We prove a Harnack inequality for the positive solutions ofa Schroedinger type equationL_0 u + V u = 0;where L_0 is an operator satisfying the Hoermander's condition 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.
A Green function and regularity results for an ultraparabolic equation with a singular potential / Polidoro, Sergio; Ragusa, M. A.. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - STAMPA. - 7:11(2002), pp. 1281-1314.
A Green function and regularity results for an ultraparabolic equation with a singular potential
POLIDORO, Sergio;
2002
Abstract
We prove a Harnack inequality for the positive solutions ofa Schroedinger type equationL_0 u + V u = 0;where L_0 is an operator satisfying the Hoermander's condition 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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