Boundary regularity for the Monge-Ampere and affine maximal surface equations

被引：107
作者：
Trudinger, Neil S. [1 ]
Wang, Xu-Jia [1 ]
机构：
[1] Australian Natl Univ, Canberra, ACT 0200, Australia
来源：
ANNALS OF MATHEMATICS | 2008年 / 167卷 / 03期
基金：
澳大利亚研究理事会;
关键词：
D O I：
10.4007/annals.2008.167.993
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove global second derivative estimates for solutions of the Dirichlet problem for the Monge-Ampere equation when the inhomogeneous term is only assumed to be Holder continuous. As a consequence of our approach, we also establish the existence and uniqueness of globally smooth solutions to the second boundary value problem for the affine maximal surface equation and affine mean curvature equation.
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页码：993 / 1028
页数：36
相关论文
共 23 条
[1]  
Blaschke W., 1923, VORLESUNGEN DIFFEREN, VII
[2]   THE DIRICHLET PROBLEM FOR NONLINEAR 2ND-ORDER ELLIPTIC-EQUATIONS .1. MONGE-AMPERE EQUATION [J].
CAFFARELLI, L ;
NIRENBERG, L ;
SPRUCK, J .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1984, 37 (03) :369-402
[3]   INTERIOR A PRIORI ESTIMATES FOR SOLUTIONS OF FULLY NON-LINEAR EQUATIONS [J].
CAFFARELLI, LA .
ANNALS OF MATHEMATICS, 1989, 130 (01) :189-213
[4]   Boundary regularity of maps with convex potentials .2. [J].
Caffarelli, LA .
ANNALS OF MATHEMATICS, 1996, 144 (03) :453-496
[5]  
Caffarelli LA, 1997, AM J MATH, V119, P423
[6]   BOUNDARY-REGULARITY OF MAPS WITH CONVEX POTENTIALS [J].
CAFFARELLI, LA .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1992, 45 (09) :1141-1151
[7]   INTERIOR W2,P ESTIMATES FOR SOLUTIONS OF THE MONGE-AMPERE EQUATION [J].
CAFFARELLI, LA .
ANNALS OF MATHEMATICS, 1990, 131 (01) :135-150
[8]   A LOCALIZATION PROPERTY OF VISCOSITY SOLUTIONS TO THE MONGE-AMPERE EQUATION AND THEIR STRICT CONVEXITY [J].
CAFFARELLI, LA .
ANNALS OF MATHEMATICS, 1990, 131 (01) :129-134
[9]   HYPERSURFACES WITH MAXIMAL AFFINELY INVARIANT AREA [J].
CALABI, E .
AMERICAN JOURNAL OF MATHEMATICS, 1982, 104 (01) :91-126
[10]  
Calabi E., 1958, MICH MATH J, V5, P105, DOI 10.1307/mmj/1028998055
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