Affine Moser-Trudinger and Morrey-Sobolev inequalities

被引：161

作者：

Cianchi, Andrea ^{[1
]}

Lutwak, Erwin ^{[2
]}

Yang, Deane ^{[2
]}

Zhang, Gaoyong ^{[2
]}

机构：

[1] Univ Florence, Dipartimento Matemat & Applicaz Architettura, I-50122 Florence, Italy

[2] NYU, Dept Math, Polytech Inst, Brooklyn, NY USA

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2009年 / 36卷 / 03期

关键词：

MINKOWSKI-FIREY THEORY; EXTREMAL-FUNCTIONS; SHARP INEQUALITY; REARRANGEMENT; OPERATORS;

D O I：

10.1007/s00526-009-0235-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An affine Moser-Trudinger inequality, which is stronger than the Euclidean Moser-Trudinger inequality, is established. In this new affine analytic inequality an affine energy of the gradient replaces the standard L-n energy of gradient. The geometric inequality at the core of the affine Moser-Trudinger inequality is a recently established affine isoperimetric inequality for convex bodies. Critical use is made of the solution to a normalized version of the L-n Minkowski Problem. An affine Morrey-Sobolev inequality is also established, where the standard L-p energy, with p > n, is replaced by the affine energy.

引用

页码：419 / 436

页数：18

共 56 条

[1]

Adams D. R., 1996, Function Spaces and Potential Theory

[2] A SHARP INEQUALITY OF MOSER,J. FOR HIGHER-ORDER DERIVATIVES [J].