Double Ball Property for non-divergence horizontally elliptic operators on step two Carnot groups | Zendy

Giulio Tralli | Zendy

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Double Ball Property for non-divergence horizontally elliptic operators on step two Carnot groups

Author(s) -

Giulio Tralli

Publication year - 2012

Publication title -

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 , property (philosophy) , ball (mathematics) , divergence (linguistics) , pure mathematics , mathematical analysis , physics , thermodynamics , philosophy , linguistics , epistemology

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

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