Hessian measures I
Hessian measures I
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DOI：
10.12775/tmna.1997.030
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发表时间：
1997-12
影响因子：
0.7
通讯作者：
N. Trudinger;Xu-jia Wang
中科院分区：
文献类型：
--
作者：
N. Trudinger;Xu-jia Wang
或者，我们可以写（1.3）Fk[u] = [Du]k，其中[A]k表示n× n矩阵A的k× k个主子式之和。本文的目的是将Fk的定义推广到相应的连续函数类，使得Fk[u]是Borel测度，并在此基础上考虑Dirichlet问题。一个函数u ∈ C（Ω）称为Ω中的k-凸（一致k-凸）函数，如果对j = 1，. . .，k.操作员Fk
Alternatively we may write (1.3) Fk[u] = [Du]k, where [A]k denotes the sum of the k× k principal minors of an n× n matrix A. Our purpose in this paper is to extend the definition of the Fk to corresponding classes of continuous functions so that Fk[u] is a Borel measure and to consider the Dirichlet problem in this setting. A function u ∈ C(Ω) is called k-convex (uniformly k-convex) in Ω if Fj [u] ≥ 0 (> 0) for j = 1, . . . , k. The operator Fk