The Dirichlet Problem for Degenerate Hessian Equations

Nina Ivochkina; Neil Trudinger; Xu Jia Wang

doi:10.1081/pde-120028851

The Dirichlet Problem for Degenerate Hessian Equations

Nina Ivochkina, Neil Trudinger^*, Xu Jia Wang

^*Corresponding author for this work

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

57 Citations (Scopus)

Abstract

In this paper, we study the Dirichlet problem for a class of fully nonlinear degenerate elliptic equations which depend only on the eigenvalues of the Hessian matrix. We provide a new and simpler approach to the estimation of second derivatives, through differentiation with respect to vector fields with skew-symmetric Jacobians.

Original language	English
Pages (from-to)	219-235
Number of pages	17
Journal	Communications in Partial Differential Equations
Volume	29
Issue number	1-2
DOIs	https://doi.org/10.1081/pde-120028851
Publication status	Published - 2005

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title = "The Dirichlet Problem for Degenerate Hessian Equations",

abstract = "In this paper, we study the Dirichlet problem for a class of fully nonlinear degenerate elliptic equations which depend only on the eigenvalues of the Hessian matrix. We provide a new and simpler approach to the estimation of second derivatives, through differentiation with respect to vector fields with skew-symmetric Jacobians.",

keywords = "Degenerate Hessian equations, Dirichlet problem, Second derivative estimates",

author = "Nina Ivochkina and Neil Trudinger and Wang, {Xu Jia}",

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AU - Trudinger, Neil

AU - Wang, Xu Jia

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KW - Degenerate Hessian equations

KW - Dirichlet problem

KW - Second derivative estimates

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DO - 10.1081/pde-120028851

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JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

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The Dirichlet Problem for Degenerate Hessian Equations

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