A variational theory of the Hessian equation

Kai Seng Chou; Xu Jia Wang

doi:10.1002/cpa.1016

A variational theory of the Hessian equation

Kai Seng Chou^*
, Xu Jia Wang

^*Corresponding author for this work

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

227 Citations (Scopus)

Abstract

By studying a negative gradient flow of certain Hessian functionals we establish the existence of critical points of the functionals and consequently the existence of ground states to a class of nonhomogenous Hessian equations. To achieve this we derive uniform, first- and second-order a priori estimates for the elliptic and parabolic Hessian equations. Our results generalize well-known results for semilinear elliptic equations and the Monge-Ampère equation.

Original language	English
Pages (from-to)	1029-1064
Number of pages	36
Journal	Communications on Pure and Applied Mathematics
Volume	54
Issue number	9
Early online date	26 Jun 2001
DOIs	https://doi.org/10.1002/cpa.1016
Publication status	Published - Sept 2001

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10.1002/cpa.1016

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title = "A variational theory of the Hessian equation",

abstract = "By studying a negative gradient flow of certain Hessian functionals we establish the existence of critical points of the functionals and consequently the existence of ground states to a class of nonhomogenous Hessian equations. To achieve this we derive uniform, first- and second-order a priori estimates for the elliptic and parabolic Hessian equations. Our results generalize well-known results for semilinear elliptic equations and the Monge-Amp{\`e}re equation.",

author = "Chou, \{Kai Seng\} and Wang, \{Xu Jia\}",

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AU - Chou, Kai Seng

AU - Wang, Xu Jia

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Y1 - 2001/9

N2 - By studying a negative gradient flow of certain Hessian functionals we establish the existence of critical points of the functionals and consequently the existence of ground states to a class of nonhomogenous Hessian equations. To achieve this we derive uniform, first- and second-order a priori estimates for the elliptic and parabolic Hessian equations. Our results generalize well-known results for semilinear elliptic equations and the Monge-Ampère equation.

AB - By studying a negative gradient flow of certain Hessian functionals we establish the existence of critical points of the functionals and consequently the existence of ground states to a class of nonhomogenous Hessian equations. To achieve this we derive uniform, first- and second-order a priori estimates for the elliptic and parabolic Hessian equations. Our results generalize well-known results for semilinear elliptic equations and the Monge-Ampère equation.

UR - https://www.scopus.com/pages/publications/0035636557

UR - http://hdl.handle.net/1885/66571

U2 - 10.1002/cpa.1016

DO - 10.1002/cpa.1016

M3 - Article

SN - 0010-3640

VL - 54

SP - 1029

EP - 1064

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 9

ER -

A variational theory of the Hessian equation

Abstract

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