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

Philippe Logaritsch and Emanuele Spadaro

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Submission date: 01. Dec. 2011
Pages: 10
published in: Communications in contemporary mathematics, 14 (2012) 6, art-no. 1250043 
DOI number (of the published article): 10.1142/S0219199712500435
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Abstract:
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.