The Lp dual Minkowski problem for p > 1 and q > 0

被引：57
作者：
Boroczky, Karoly J. [1 ,2 ]
Fodor, Ferenc [3 ]
机构：
[1] Hungarian Acad Sci, Alfred Renyi Inst Math, Realtanoda U 13-15, H-1053 Budapest, Hungary
[2] Cent European Univ, Dept Math, Nador U 9, H-1051 Budapest, Hungary
[3] Univ Szeged, Dept Geometry, Bolyai Inst, Aradi Vertanuk Tere 1, H-6720 Szeged, Hungary
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2019年 / 266卷 / 12期
关键词：
L-p dual Minkowski problem; Monge-Ampere equation;
D O I：
10.1016/j.jde.2018.12.020
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
General L-p dual curvature measures have recently been introduced by Lutwak, Yang and Zhang [24]. These new measures unify several other geometric measures of the Brunn-Minkowski theory and the dual Brunn-Minkowski theory. L-p dual curvature measures arise from qth dual intrinsic volumes by means of Alexandrov-type variational formulas. Lutwak, Yang and Zhang [24] formulated the L-p dual Minkowski problem, which concerns the characterization of L-p dual curvature measures. In this paper, we solve the existence part of the L-p dual Minkowski problem for p > 1 and q > 0, and we also discuss the regularity of the solution. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码：7980 / 8033
页数：54
相关论文
共 32 条
[1]  
ALEKSANDROV A., 1939, Mat. Sb., V6, P167
[2]  
Aleksandrov A., 1938, Mat. Sb. (N.S.), V3, P27
[3]  
[Anonymous], 2007, GRUNDLEHREN MATH WIS
[4]  
[Anonymous], 2008, Adv. Lect. Math. (ALM)
[5]  
Artin Emil, 1964, SELECT TOPICS MATH
[6]  
Böröczky KJ, 2013, J AM MATH SOC, V26, P831
[7]  
Boroczky Karoly J., ARXIV170306259
[8]   INTERIOR W2,P ESTIMATES FOR SOLUTIONS OF THE MONGE-AMPERE EQUATION [J].
CAFFARELLI, LA .
ANNALS OF MATHEMATICS, 1990, 131 (01) :135-150
[9]   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
[10]   THE LOGARITHMIC MINKOWSKI PROBLEM FOR NON-SYMMETRIC MEASURES [J].
Chen, Shibing ;
Li, Qi-Rui ;
Zhu, Guangxian .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 371 (04) :2623-2641
1234