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.
Publié le : 2008-04-15
Classification:
hypoelliptic operator,
Schrödinger equation,
Harnack inequality,
Green function,
35K70,
35J10,
35K20,
32A37,
35B65
@article{1228834303,
author = {Polidoro
,
Sergio and Ragusa
,
Maria Alessandra},
title = {Harnack inequality for hypoelliptic ultraparabolic equations
with a singular lower order term},
journal = {Rev. Mat. Iberoamericana},
volume = {24},
number = {2},
year = {2008},
pages = { 1011-1046},
language = {en},
url = {http://dml.mathdoc.fr/item/1228834303}
}
Polidoro
,
Sergio; Ragusa
,
Maria Alessandra. Harnack inequality for hypoelliptic ultraparabolic equations
with a singular lower order term. Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, pp. 1011-1046. http://gdmltest.u-ga.fr/item/1228834303/