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

作者：Tralli Giulio^*

来源：Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, 2012, 23(4): 351-360.

DOI：10.4171/RLM/632

• Degenerate elliptic equation
• invariant Harnack inequality
• double ball property

Let L be a linear second order horizontally elliptic operator on a Carnot group of step two. We assume L in non-divergence form and with measurable coefficients. Then, we prove the Double Ball Property for the nonnegative sub-solutions of 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 epsilon-Critical Density.

• 出版日期2012