New isoperimetric estimates for solutions to Monge-Ampere equations

被引：19
|
作者：
Brandolini, B. [1 ]
Nitsch, C. [1 ]
Trombetti, C. [1 ]
机构：
[1] Univ Naples Federico 2, Dipartimento Matemat & Applicaz R Caccioppoli, I-80126 Naples, Italy
来源：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2009年 / 26卷 / 04期
关键词：
Affine isoperimetric inequalities; Monge-Ampere equation; SYMMETRIZATION; REARRANGEMENTS; INEQUALITIES; REAL;
D O I：
10.1016/j.anihpc.2008.09.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove some sharp estimates for solutions to Dirichlet problems relative to Monge-Ampere equations. Among them we show that the eigenvalue of the Dirichlet problem, when computed on convex domains with fixed measure, is maximal on ellipsoids. This result falls in the class of affine isoperimetric inequalities and shows that the eigenvalue of the Monge-Ampere operator behaves just the contrary of the first eigenvalue of the Laplace operator. (C) 2008 Elsevier Masson SAS. All rights reserved.
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页码：1265 / 1275
页数：11
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