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A representation formula for the p-Energy of metric space valued Sobolev maps

Philippe Logaritsch and Emanuele Spadaro


We give an explicit representation formula for the $p$-energy of Sobolev maps with values in a metric space as defined by Korevaar and Schoen (Comm. Anal. Geom. 1 (1993), no. 3-4, 561--659). The formula is written in terms of the Lipschitz compositions introduced by Ambrosio (Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1990), n. 17, 439--478), thus further relating the two different definitions considered in the literature.

Dec 1, 2011
Dec 5, 2011

Related publications

2012 Repository Open Access
Philippe Logaritsch and Emanuele Spadaro

A representation formula for the p-energy of metric space-valued Sobolev maps

In: Communications in contemporary mathematics, 14 (2012) 6, p. 1250043