Hessian measures II

Research Report MRR97-035

Hessian measures II

Neil S. Trudinger, Xu-Jia Wang

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 $\Omega$ in Euclidean n-space, $k=1, \cdots, n$ , 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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