Affine Moser-Trudinger and Morrey-Sobolev inequalities
Affine Moser-Trudinger and Morrey-Sobolev inequalities
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DOI：
10.1007/s00526-009-0235-4
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发表时间：
2009-11-01
影响因子：
2.1
通讯作者：
Zhang, Gaoyong
中科院分区：
文献类型：
--
作者：
Cianchi, Andrea;Lutwak, Erwin;Zhang, Gaoyong
建立了一个比欧几里得Moser-Trudinger不等式更强的仿射Moser-Trudinger不等式。在这个新的仿射解析不等式中，梯度的仿射能量代替了标准的L-n梯度能量。仿射Moser-Trudinger不等式的核心是最近建立的凸体仿射等周不等式。对L-n-Minkowski问题的一个归一化版本的解进行了关键的使用。还建立了一个仿射Morrey-Sobolev不等式，其中用仿射能量代替标准L-p能量与p>；n。
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.