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.
Harnack's inequality for a class of non-divergent equations in the Heisenberg group
Tralli, Giulio
2017
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 developed by Di Fazio, Gutiérrez, and Lanconelli to obtain Harnack’s inequality.File in questo prodotto:
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