Affine Moser-trudinger and Morrey-sobolev inequalities

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Abstract

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 Ln 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 Ln Minkowski Problem. An affine Morrey-Sobolev inequality is also established, where the standard Lp energy, with p > n, is replaced by the affine energy.

Original languageEnglish (US)
Pages (from-to)419-436
Number of pages18
JournalCalculus of Variations and Partial Differential Equations
Volume36
Issue number3
DOIs
Publication statusPublished - Oct 2009

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ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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