We consider second order linear degenerate-elliptic operators which are elliptic with respect to horizontal directions generating a stratified algebra of H-type. Extending a result by Gutiérrez and Tournier (2011) for the Heisenberg group, we prove a critical density estimate by assuming a condition of Cordes-Landis type. We then deduce an invariant Harnack inequality for the non-negative solutions from a result by Di Fazio, Gutiérrez, and Lanconelli (2008).
Giulio Tralli (2014). A certain critical density property for invariant Harnack inequalities in H-type groups. JOURNAL OF DIFFERENTIAL EQUATIONS, 256, 461-474 [10.1016/j.jde.2013.09.008].
A certain critical density property for invariant Harnack inequalities in H-type groups
TRALLI, GIULIO
2014
Abstract
We consider second order linear degenerate-elliptic operators which are elliptic with respect to horizontal directions generating a stratified algebra of H-type. Extending a result by Gutiérrez and Tournier (2011) for the Heisenberg group, we prove a critical density estimate by assuming a condition of Cordes-Landis type. We then deduce an invariant Harnack inequality for the non-negative solutions from a result by Di Fazio, Gutiérrez, and Lanconelli (2008).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
