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Harnack’s inequality for a class of non-divergent equations in the Heisenberg group

Abedin, F
; 
Gutiérrez, CE
; 
Tralli, G
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Pre-print
Date
2017-10-03
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Apriori estimates
 subelliptic equations
 symplectic matrices
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http://hdl.handle.net/20.500.12613/4878
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1705.10856v1.pdf
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DOI
10.1080/03605302.2017.1384836
Abstract
© 2017 Taylor & Francis. We prove an invariant Harnack’s inequality for operators in non-divergence form structured on Heisenberg vector fields when the coefficient matrix is uniformly positive definite, continuous, and symplectic. The method consists in constructing appropriate barriers to obtain pointwise-to-measure estimates for supersolutions in small balls, and then invoking the axiomatic approach developed by Di Fazio, Gutiérrez, and Lanconelli to obtain Harnack’s inequality.
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Informa UK Limited
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Communications in Partial Differential Equations
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