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.
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U2 - 10.1007/BF02560581
DO - 10.1007/BF02560581
M3 - Article
AN - SCOPUS:51649155409
VL - 4
SP - 250
EP - 265
JO - Acta Mathematica Sinica, English Series
JF - Acta Mathematica Sinica, English Series
SN - 1439-8516
IS - 3
ER -