Calculus of Variations and Geometric Measure Theory

E. Acerbi - D. Mucci

Graphs of maps between manifolds in trace spaces and with vanishing mean oscillation

created by mucci on 06 Nov 2012
modified on 24 Sep 2014


Published Paper

Inserted: 6 nov 2012
Last Updated: 24 sep 2014

Journal: Annales de l'Institut Henri Poincaré / Analyse non linéaire
Volume: 31
Pages: 1015--1034
Year: 2014
Doi: 10.1016/j.anihpc.2013.07.010


We give a positive answer to a question raised by Alberti in connection with a recent result by Brezis-Nguyen. We show the existence of currents associated with graphs of maps in trace spaces that have vanishing mean oscillation. The degree of such maps may be written in terms of these currents, of which we give some structure properties. We also deal with relevant examples.