TY - JOUR
T1 - Affine Moser-trudinger and Morrey-sobolev inequalities
AU - Cianchi, Andrea
AU - Lutwak, Erwin
AU - Yang, Deane
AU - Zhang, Gaoyong
PY - 2009/10
Y1 - 2009/10
N2 - 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.
AB - 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.
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U2 - 10.1007/s00526-009-0235-4
DO - 10.1007/s00526-009-0235-4
M3 - Article
AN - SCOPUS:70350389542
SN - 0944-2669
VL - 36
SP - 419
EP - 436
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 3
ER -