GLOBAL SOLUTIONS AND EXTERIOR DIRICHLET PROBLEM FOR MONGE-AMPERE EQUATION IN R2

被引：0

作者：

Bao, Jiguang ^{[1
]}

Li, Haigang ^{[1
]}

Zhang, Lei ^{[2
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

[2] Univ Florida, Dept Math, 358 Little Hall,POB 118105, Gainesville, FL 32611 USA

来源：

DIFFERENTIAL AND INTEGRAL EQUATIONS | 2016年 / 29卷 / 5-6期

关键词：

EXTENSION; THEOREM;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Monge-Ampere equation det(D(2)u) = f in two dimensional spaces is different in nature from their counterparts in higher dimensional spaces. In this article we employ new ideas to establish two main results for the Monge-Ampere equation defined either globally in R-2 or outside a convex set. First, we prove the existence of a global solution that satisfies a prescribed asymptotic behavior at infinity, if f is asymptotically close to a positive constant. Then we solve the exterior Dirichlet problem if data are given on the boundary of a convex set and at infinity.

引用

页码：563 / 582

页数：20

共 26 条

[1] Aleksandrov A.D., 1958, Vestn. Leningr. Univ., V13, P5
[2] [Anonymous], 1963, Ann. Scuola Norm. Sup. Pisa Cl. Sci.
[3] BAKELMAN IJ, 1957, DOKL AKAD NAUK SSSR+, V114, P1143
[4] Monge-Ampere equation on exterior domains
Bao, Jiguang
Li, Haigang
Zhang, Lei
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 52 (1-2) : 39 - 63
[5] On the exterior Dirichlet problem for the Monge-Ampere equation in dimension two
Bao, Jiguang
Li, Haigang
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (18) : 6448 - 6455
[6] THE DIRICHLET PROBLEM FOR NONLINEAR 2ND-ORDER ELLIPTIC-EQUATIONS .1. MONGE-AMPERE EQUATION
CAFFARELLI, L
NIRENBERG, L
SPRUCK, J
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1984, 37 (03) : 369 - 402
[7] An extension to a theorem of Jorgens, Calabi, and Pogorelov
Caffarelli, L
Li, YY
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2003, 56 (05) : 549 - 583
[8] Caffarelli L., 1995, Topics in PDEs: The Monge-Ampere equation
[9] Caffarelli Luis A, 1995, AM MATH SOC C PUBLIC, V43, P104
[10] Calabi E., 1958, MICH MATH J, V5, P105, DOI 10.1307/mmj/1028998055

← 1 2 3 →