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On Hessian measures for non-commuting vector fields

Neil S Trudinger
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Abstract

Previous results on Hessian measures by Trudinger and Wang are extended to the subelliptic case. Specifically we prove the weak continuity of the 2-Hessian operator, with respect to local L1 convergence, for a system of m vector fields of step 2 and derive gradient estimates for the corresponding k-convex functions, k=1,2....m, for arbitrary step.

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Neil S Trudinger. 2005-07-13. On Hessian measures for non-commuting vector fields. https://arxiv.org/abs/math/0503695

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