Hessian measures III

Neil S. Trudinger; Xu Jia Wang

doi:10.1006/jfan.2001.3925

Hessian measures III

Neil S. Trudinger^*
, Xu Jia Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

83 Citations (SciVal)

Abstract

In this paper, we continue previous investigations into the theory of Hessian measures. We extend our weak continuity result to the case of mixed k-Hessian measures associated with k-tuples of k-convex functions, on domains in Euclidean n-space, k = 1, 2,⋯,n. Applications are given to capacity, quasicontinuity, and the Dirichlet problem, with inhomogeneous terms, continuous with respect to capacity or combinations of Dirac measures.

Original language	English
Pages (from-to)	1-23
Number of pages	23
Journal	Journal of Functional Analysis
Volume	193
Issue number	1
DOIs	https://doi.org/10.1006/jfan.2001.3925
Publication status	Published - 1 Aug 2002

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title = "Hessian measures III",

abstract = "In this paper, we continue previous investigations into the theory of Hessian measures. We extend our weak continuity result to the case of mixed k-Hessian measures associated with k-tuples of k-convex functions, on domains in Euclidean n-space, k = 1, 2,⋯,n. Applications are given to capacity, quasicontinuity, and the Dirichlet problem, with inhomogeneous terms, continuous with respect to capacity or combinations of Dirac measures.",

keywords = "Dirichlet problem, Hessian capacities, Hessian measures, Weak convergence",

author = "Trudinger, \{Neil S.\} and Wang, \{Xu Jia\}",

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AU - Wang, Xu Jia

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N2 - In this paper, we continue previous investigations into the theory of Hessian measures. We extend our weak continuity result to the case of mixed k-Hessian measures associated with k-tuples of k-convex functions, on domains in Euclidean n-space, k = 1, 2,⋯,n. Applications are given to capacity, quasicontinuity, and the Dirichlet problem, with inhomogeneous terms, continuous with respect to capacity or combinations of Dirac measures.

AB - In this paper, we continue previous investigations into the theory of Hessian measures. We extend our weak continuity result to the case of mixed k-Hessian measures associated with k-tuples of k-convex functions, on domains in Euclidean n-space, k = 1, 2,⋯,n. Applications are given to capacity, quasicontinuity, and the Dirichlet problem, with inhomogeneous terms, continuous with respect to capacity or combinations of Dirac measures.

KW - Dirichlet problem

KW - Hessian capacities

KW - Hessian measures

KW - Weak convergence

UR - https://www.scopus.com/pages/publications/0036695926

U2 - 10.1006/jfan.2001.3925

DO - 10.1006/jfan.2001.3925

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VL - 193

SP - 1

EP - 23

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

Hessian measures III

Abstract

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