Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint
77/2011

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

Philippe Logaritsch and Emanuele Spadaro

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.

Received:
Dec 1, 2011
Published:
Dec 5, 2011

Related publications

inJournal
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