JournalsrlmVol. 23, No. 4pp. 351–360

Double Ball Property for non-divergence horizontally elliptic operators on step two Carnot groups

  • Giulio Tralli

    Università di Bologna, Italy
Double Ball Property for non-divergence horizontally elliptic operators on step two Carnot groups cover
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Abstract

Let L\mathcal L be a linear second order horizontally elliptic operator on a Carnot group of step two. We assume L\mathcal L in non-divergence form and with measurable coefficients. Then, we prove the Double Ball Property for the nonnegative sub-solutions of L\mathcal L. With our result, in order to solve the Harnack inequality problem for this kind of operators, it becomes sufficient to prove the so called ϵ\epsilon-Critical Density.

Cite this article

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. 351–360

DOI 10.4171/RLM/632