Hessian measures II

• 成果类型: Article
• 署名作者: Trudinger, NS; Wang, XJ
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/121089
• 发表日期: 1999
• 页码: 579-604
• 关键词: nonlinear elliptic-equations; monge-ampere equation; dirichlet problem; VISCOSITY SOLUTIONS; EXISTENCE

摘要

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,, n, and proved a weak continuity result with respect to local uniform convergence. In this paper, we consider L-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.