Let be a linear second order horizontally elliptic operator on a Carnot group of step two. We assume in non-divergence form and with measurable coefficients. Then, we prove the Double Ball Property for the nonnegative sub-solutions of . With our result, in order to solve the Harnack inequality problem for this kind of operators, it becomes sufficient to prove the so called -Critical Density.
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Giulio Tralli, Double Ball Property for non-divergence horizontally elliptic operators on step two Carnot groups. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 23 (2012), no. 4, pp. 351–360DOI 10.4171/RLM/632