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

72 Citations (Scopus)

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

Access to Document

10.1006/jfan.2001.3925

Cite this

@article{2d9bf2f8dd07463d872df17da57162a6,

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}",

year = "2002",

month = aug,

day = "1",

doi = "10.1006/jfan.2001.3925",

language = "English",

volume = "193",

pages = "1--23",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Hessian measures III

AU - Trudinger, Neil S.

AU - Wang, Xu Jia

PY - 2002/8/1

Y1 - 2002/8/1

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 - http://www.scopus.com/inward/record.url?scp=0036695926&partnerID=8YFLogxK

U2 - 10.1006/jfan.2001.3925

DO - 10.1006/jfan.2001.3925

M3 - Article

SN - 0022-1236

VL - 193

SP - 1

EP - 23

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

Hessian measures III

Abstract

Access to Document

Other files and links

Fingerprint

Cite this