On the existence of solutions of a class of Monge-Ampére equations

Gang Tian

doi:10.1007/BF02560581

On the existence of solutions of a class of Monge-Ampére equations

Gang Tian

Mathematics

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

21 Scopus citations

Abstract

In this paper, the Dirichlet problem for the Monge-Ampére equation det(u_ij)=F(x,u,Δu) on a convex bounded domain ΩσR″ is considered. The author establishes a new C^o-estimate and gives some new existence results. He also presents a new proof for the C^3,α-estimates of solutions, which not only weakens the smooth assumptions for F but also applies to more general nonlinear elliptic systems.

Original language	English (US)
Pages (from-to)	250-265
Number of pages	16
Journal	Acta Mathematica Sinica
Volume	4
Issue number	3
DOIs	https://doi.org/10.1007/BF02560581
State	Published - Sep 1 1988

All Science Journal Classification (ASJC) codes

Mathematics(all)

Access to Document

10.1007/BF02560581

Cite this

@article{3a8097f39db74d88a34b009ddaf03b4d,

title = "On the existence of solutions of a class of Monge-Amp{\'e}re equations",

abstract = "In this paper, the Dirichlet problem for the Monge-Amp{\'e}re equation det(u ij)=F(x,u,Δu) on a convex bounded domain ΩσR″ is considered. The author establishes a new C o-estimate and gives some new existence results. He also presents a new proof for the C 3,α-estimates of solutions, which not only weakens the smooth assumptions for F but also applies to more general nonlinear elliptic systems.",

author = "Gang Tian",

year = "1988",

month = sep,

day = "1",

doi = "10.1007/BF02560581",

language = "English (US)",

volume = "4",

pages = "250--265",

journal = "Acta Mathematica Sinica",

issn = "1439-8516",

publisher = "Springer Verlag",

number = "3",

}

TY - JOUR

T1 - On the existence of solutions of a class of Monge-Ampére equations

AU - Tian, Gang

PY - 1988/9/1

Y1 - 1988/9/1

N2 - In this paper, the Dirichlet problem for the Monge-Ampére equation det(u ij)=F(x,u,Δu) on a convex bounded domain ΩσR″ is considered. The author establishes a new C o-estimate and gives some new existence results. He also presents a new proof for the C 3,α-estimates of solutions, which not only weakens the smooth assumptions for F but also applies to more general nonlinear elliptic systems.

AB - In this paper, the Dirichlet problem for the Monge-Ampére equation det(u ij)=F(x,u,Δu) on a convex bounded domain ΩσR″ is considered. The author establishes a new C o-estimate and gives some new existence results. He also presents a new proof for the C 3,α-estimates of solutions, which not only weakens the smooth assumptions for F but also applies to more general nonlinear elliptic systems.

UR - http://www.scopus.com/inward/record.url?scp=51649155409&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51649155409&partnerID=8YFLogxK

U2 - 10.1007/BF02560581

DO - 10.1007/BF02560581

M3 - Article

AN - SCOPUS:51649155409

SN - 1439-8516

VL - 4

SP - 250

EP - 265

JO - Acta Mathematica Sinica

JF - Acta Mathematica Sinica

IS - 3

ER -

On the existence of solutions of a class of Monge-Ampére equations

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this