On Hessian measures for non-commuting vector fields

2005/03/30 by Neil S. Trudinger, Neil S Trudinger, Trudinger, Neil S
Mathematics · #28A33 #35H20 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #msc:28A33 #msc:35H20

paper · pdf · doi:10.48550/arxiv.math/0503695

Minor changes and some extra references

openalex publication_date 2005/03/30 · arxiv created 2005/07/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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