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Hessian Measures II

Neil S. Trudinger and Xu-Jia Wang
Annals of Mathematics
Second Series, Vol. 150, No. 2 (Sep., 1999), pp. 579-604
Published by: Annals of Mathematics
DOI: 10.2307/121089
Stable URL: http://www.jstor.org/stable/121089
Page Count: 26
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Hessian Measures II
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Abstract

In our previous paper on this topic, we introduced the notion of k-Hessian measure associated with a continuous k-convex function in a domain Ω in Euclidean n-space, k = 1,..., n, and proved a weak continuity result with respect to local uniform convergence. In this paper, we consider k-convex functions, not necessarily continuous, and prove the weak continuity of the associated k-Hessian measure with respect to convergence in measure. The proof depends upon local integral estimates for the gradients of k-convex functions.

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