arXiv subjects

Ezequiel R. Barbosa

Publications and source records attributed to Ezequiel R. Barbosa.

2 recordsLinked to original sources

arXiv2010

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

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.

math.AP↗

arXiv2008

On the geometric dependence of Riemannian Sobolev best constants

We concerns here with the continuity on the geometry of the second Riemannian L^p-Sobolev best constant B_0(p,g) associated to the AB program. Precisely, for 1 <= p <= 2, we prove that B_0(p,g) depends continuously on g in the C^2-topology. Moreover, this topology is sharp for p = 2. From this discussion, we deduce some existence and C^0-compactness results on extremal functions.

math.DG↗