Moser-Trudinger type inequalities for the Hessian equation

Gu Ji Tian; Xu Jia Wang

doi:10.1016/j.jfa.2010.06.009

Moser-Trudinger type inequalities for the Hessian equation

Gu Ji Tian^*
, Xu Jia Wang

^*Corresponding author for this work

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

24 Citations (Scopus)

Abstract

The k-Hessian equation for k≥2 is a class of fully nonlinear partial differential equation of divergence form. A Sobolev type inequality for the k-Hessian equation was proved by the second author in 1994. In this paper, we prove the Moser-Trudinger type inequality for the k-Hessian equation.

Original language	English
Pages (from-to)	1974-2002
Number of pages	29
Journal	Journal of Functional Analysis
Volume	259
Issue number	8
DOIs	https://doi.org/10.1016/j.jfa.2010.06.009
Publication status	Published - Oct 2010

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10.1016/j.jfa.2010.06.009

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title = "Moser-Trudinger type inequalities for the Hessian equation",

abstract = "The k-Hessian equation for k≥2 is a class of fully nonlinear partial differential equation of divergence form. A Sobolev type inequality for the k-Hessian equation was proved by the second author in 1994. In this paper, we prove the Moser-Trudinger type inequality for the k-Hessian equation.",

keywords = "A priori estimates, Hessian equation, Moser-Trudinger inequality",

author = "Tian, \{Gu Ji\} and Wang, \{Xu Jia\}",

year = "2010",

month = oct,

doi = "10.1016/j.jfa.2010.06.009",

language = "English",

volume = "259",

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journal = "Journal of Functional Analysis",

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T1 - Moser-Trudinger type inequalities for the Hessian equation

AU - Tian, Gu Ji

AU - Wang, Xu Jia

PY - 2010/10

Y1 - 2010/10

N2 - The k-Hessian equation for k≥2 is a class of fully nonlinear partial differential equation of divergence form. A Sobolev type inequality for the k-Hessian equation was proved by the second author in 1994. In this paper, we prove the Moser-Trudinger type inequality for the k-Hessian equation.

AB - The k-Hessian equation for k≥2 is a class of fully nonlinear partial differential equation of divergence form. A Sobolev type inequality for the k-Hessian equation was proved by the second author in 1994. In this paper, we prove the Moser-Trudinger type inequality for the k-Hessian equation.

KW - A priori estimates

KW - Hessian equation

KW - Moser-Trudinger inequality

UR - https://www.scopus.com/pages/publications/77955515110

U2 - 10.1016/j.jfa.2010.06.009

DO - 10.1016/j.jfa.2010.06.009

M3 - Article

SN - 0022-1236

VL - 259

SP - 1974

EP - 2002

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 8

ER -

Moser-Trudinger type inequalities for the Hessian equation

Abstract

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