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.
Double Ball Property for non-divergence horizontally elliptic operators on step two Carnot groups / Tralli, Giulio. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - STAMPA. - 23:4(2012), pp. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.