Affine Moser-Trudinger and Morrey-Sobolev inequalities
نویسندگان
چکیده
Abstract: An affine Moser-Trudinger inequality, which is stronger than the Euclidean MoserTrudinger inequality, is established. In this new affine analytic inequality an affine energy of the gradient replaces the standard L 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 Minkowski Problem. An affine Morrey-Sobolev inequality is also established, where the standard L energy, with p > n, is replaced by the affine energy.
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