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 ε-Critical Density.
Giulio Tralli (2012). Double Ball Property for non-divergence horizontally elliptic operators on step two Carnot groups. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, 23, 351-360 [10.4171/RLM/632].
Double Ball Property for non-divergence horizontally elliptic operators on step two Carnot groups
TRALLI, GIULIO
2012
Abstract
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 ε-Critical Density.File in questo prodotto:
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