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

63 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\}",

year = "2005",

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AU - Trudinger, Neil

AU - Wang, Xu Jia

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AB - 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.

KW - Degenerate Hessian equations

KW - Dirichlet problem

KW - Second derivative estimates

UR - https://www.scopus.com/pages/publications/1642310857

U2 - 10.1081/pde-120028851

DO - 10.1081/pde-120028851

M3 - Article

SN - 0360-5302

VL - 29

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EP - 235

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 1-2

ER -

The Dirichlet Problem for Degenerate Hessian Equations

Abstract

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