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September, 2002 Sharp Affine LP Sobolev Inequalities
Erwin Lutwak, Deane Yang, Gaoyong Zhang
J. Differential Geom. 62(1): 17-38 (September, 2002). DOI: 10.4310/jdg/1090425527

Abstract

A sharp affine Lp Sobolev inequality for functions on Euclidean n-space is established. This new inequality is significantly stronger than (and directly implies) the classical sharp Lp Sobolev inequality of Aubin and Talenti, even though it uses only the vector space structure and standard Lebesgue measure on ℝn. For the new inequality, no inner product, norm, or conformal structure is needed; the inequality is invariant under all affine transformations of ℝn.

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Erwin Lutwak. Deane Yang. Gaoyong Zhang. "Sharp Affine LP Sobolev Inequalities." J. Differential Geom. 62 (1) 17 - 38, September, 2002. https://doi.org/10.4310/jdg/1090425527

Information

Published: September, 2002
First available in Project Euclid: 21 July 2004

zbMATH: 1073.46027
MathSciNet: MR1987375
Digital Object Identifier: 10.4310/jdg/1090425527

Rights: Copyright © 2002 Lehigh University

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Vol.62 • No. 1 • September, 2002
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