TITLE

# Affine Moserâ€“Trudinger and Morreyâ€“Sobolev inequalities

AUTHOR(S)
Cianchi, Andrea; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong
PUB. DATE
November 2009
SOURCE
Calculus of Variations & Partial Differential Equations;Nov2009, Vol. 36 Issue 3, p419
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
An affine Moserâ€“Trudinger inequality, which is stronger than the Euclidean Moserâ€“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 Moserâ€“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 Morreyâ€“Sobolev inequality is also established, where the standard L p energy, with p > n, is replaced by the affine energy.
ACCESSION #
44500040

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