Extremal maps in best constants vector theory - Part I: Duality and Compactness

Details Extremal maps in best constants vector theory - Part I: Duality and Compactness Extremal maps in best constants vector theory - Part I: Duality and Compactness

2010-11-04

arxiv.org/abs/1011.1037v2

Mathematics

Analysis of PDEs

Scientific paper

We develop a comprehensive study on sharp potential type Riemannian Sobolev inequalities of order 2 by means of a local geometric Sobolev inequality of same kind and suitable De Giorgi-Nash-Moser estimates. In particular we discuss questions like continuous dependence of optimal constants and existence and compactness of extremal maps. The main obstacle arising in the present setting lies at fairly weak conditions of regularity assumed on potential functions.

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