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

页码：268 / 280

页数：13

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