arXiv:1705.10856 Abstract | arXiv Analytics

arXiv:1705.10856 [math.AP]Abstract References Reviews Resources

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

Farhan Abedin, Cristian E. Gutiérrez, Giulio Tralli

Published 2017-05-30Version 1

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 from [DGL08] to obtain Harnack's inequality.

Categories: math.AP

Keywords: heisenberg group, non-divergent equations, invariant harnacks inequality, heisenberg vector fields, axiomatic approach

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