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arXiv · 1705.10856

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

Farhan Abedin·Cristian E. Gutiérrez·Giulio Tralli
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Abstract

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.

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Farhan Abedin, Cristian E. Gutiérrez, Giulio Tralli. 2017-05-30. Harnack's inequality for a class of non-divergent equations in the Heisenberg group. https://arxiv.org/abs/1705.10856

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