Open AccessDouble Ball Property for non-divergence horizontally elliptic operators on step two Carnot groups
Author(s) -
Giulio Tralli
Publication year - 2012
Publication title -
atti della accademia nazionale dei lincei. rendiconti lincei. matematica e applicazioni
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.824
H-Index - 28
eISSN - 1720-0768
pISSN - 1120-6330
DOI - 10.4171/rlm/632
Subject(s) - carnot cycle , mathematics , harnack's inequality , ball (mathematics) , elliptic operator , divergence (linguistics) , operator (biology) , pure mathematics , order (exchange) , property (philosophy) , mathematical analysis , physics , quantum mechanics , linguistics , philosophy , biochemistry , chemistry , finance , repressor , epistemology , gene , transcription factor , economics
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