We investigate the notion of the so-called Double Ball Property, which concerns the nonnegative sub-solutions of some differential operators. Thanks to the axiomatic approach developed in [6], this is an important tool in order to solve the Krylov-Safonov's Harnack inequality problem for this kind of operators. In particular, we are interested in linear second order horizontally-elliptic operators in non-divergence formand with measurable coefficients. In the setting of homogeneous Carnot groups, we would like to stress the relation between the Double Ball Property and a kind of solvability of the Dirichlet problem for the operator in the exterior of some homogeneous balls. We present a recent result obtained in [15], where the double ball property has been proved in a generic Carnot group of step two.
@article{3417,
title = {Double ball property: an overview and the case of step two Carnot groups},
journal = {Bruno Pini Mathematical Analysis Seminar},
year = {2012},
doi = {10.6092/issn.2240-2829/3417},
language = {EN},
url = {http://dml.mathdoc.fr/item/3417}
}
Tralli, Giulio. Double ball property: an overview and the case of step two Carnot groups. Bruno Pini Mathematical Analysis Seminar, (2012), . doi : 10.6092/issn.2240-2829/3417. http://gdmltest.u-ga.fr/item/3417/