Event Date
2011-10-31
Event Time
02:30 pm ~ 03:20 pm
Event Location
Wachman 617
Abstract: In joint work with Federico Tournier, we obtain an invariant Harnacks inequality for non negative solutions to degenerate elliptic equations of the form \[a(x; y; z)X1; 1u + 2b(x; y; z)X1; 2u + c(x; y; z)X2; 2u = 0,\] where $Xi; j$ are dened with the Heisenberg vector fields and the matrix coefficient is uniformly elliptic, and satisfying the additional condition that the ratio between the maximum and minimum eigenvalues is sufficiently close to one. In the paper we prove critical density and double ball estimates, once this is established, Harnack follows directly from the results of Gutierrez, Lanconelli and Di Fazio, Mathema- tishe Annalen, 2008. Preprint available at http://math.temple.edu/~gutierre/papers/harnack.subelliptic.final.version.june.28.2011.pdf