MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

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.


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