On the regularity of the Lp Minkowski problem

被引：33
|
作者：
Huang, Yong [1 ]
Lu, QiuPing [2 ]
机构：
[1] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China
[2] Ctr Modelamiento Matemat, Santiago, Chile
来源：
ADVANCES IN APPLIED MATHEMATICS | 2013年 / 50卷 / 02期
关键词：
L-p-Minkowski problems; Monge-Ampere equation; Regularity; EVOLVING PLANE-CURVES; FIREY THEORY; AFFINE; CURVATURE; SHAPES;
D O I：
10.1016/j.aam.2012.08.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The L-p Minkowski problem is equivalent to solve the Monge-Ampere equation det(u(ij) + u delta(ij)) = u(p-1) f, on S-n. Since it is degenerate for 1 < p < n + 1, the equation has no smooth solution even when the prescribed positive function f is smooth. In this paper, the C-infinity regularity for the solution is obtained for 2 < p < n + 1 by adding a gradient condition on f. (c) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：268 / 280
页数：13
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