A Dirichlet's principle for the k-Hessian

Research output: Contribution to journalArticle

Abstract

The k-Hessian operator σ k is the k-th elementary symmetric function of the eigenvalues of the Hessian. It is known that the k-Hessian equation σ k (D 2 u)=f with Dirichlet boundary condition u=0 is variational; indeed, this problem can be studied by means of the k-Hessian energy −∫uσ k (D 2 u). We construct a natural boundary functional which, when added to the k-Hessian energy, yields as its critical points solutions of k-Hessian equations with general non-vanishing boundary data. As a consequence, we establish a Dirichlet's principle for k-admissible functions with prescribed Dirichlet boundary data.

Original languageEnglish (US)
Pages (from-to)2895-2916
Number of pages22
JournalJournal of Functional Analysis
Volume275
Issue number11
DOIs
StatePublished - Dec 1 2018

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Dirichlet
Elementary Symmetric Functions
Energy
Dirichlet Boundary Conditions
Critical point
Eigenvalue
Operator

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

Case, Jeffrey Steven ; Wang, Yi. / A Dirichlet's principle for the k-Hessian. In: Journal of Functional Analysis. 2018 ; Vol. 275, No. 11. pp. 2895-2916.
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A Dirichlet's principle for the k-Hessian. / Case, Jeffrey Steven; Wang, Yi.

In: Journal of Functional Analysis, Vol. 275, No. 11, 01.12.2018, p. 2895-2916.

Research output: Contribution to journalArticle

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