Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 36, 2011, 393-410

LOWER SEMICONTINUOUS FUNCTIONALS FOR ALMGREN'S MULTIPLE VALUED FUNCTIONS

Camillo De Lellis, Matteo Focardi and Emanuele Nunzio Spadaro

Universität Zürich, Institut für Mathematik
Winterthurerstrasse 190, CH-8057 Zürich, Schweiz; camillo.delellis 'at' math.uzh.ch

Università di Firenze, Dipartimento di Matematica "Ulisse Dini"
Viale Morgagni, 67/a, 50134 Firenze, Italia; focardi 'at' math.unifi.it

Universität Bonn, Hausdorff Center for Mathematics
Villa Maria, Endenicher Allee 62, D-53115 Bonn, Germany; emanuele.spadaro 'at' hcm.uni-bonn.de

Abstract. We consider general integral functionals on the Sobolev spaces of multiple valued functions introduced by Almgren. We characterize the semicontinuous ones and recover earlier results of Mattila in [10] as a particular case. Moreover, we answer positively to one of the questions raised by Mattila in the same paper.

2010 Mathematics Subject Classification: Primary 49J45, 49Q20.

Key words: Q-valued functions, semicontinuity, quasiconvexity, Q-ellipticity.

Reference to this article: C. De Lellis, M. Focardi and E.N. Spadaro: Lower semicontinuous functionals for Almgren's multiple valued functions. Ann. Acad. Sci. Fenn. Math. 36 (2011), 393-410.

Full document as PDF file

doi:10.5186/aasfm.2011.3626