Lower semicontinuous functionals for Almgren's multiple valued functions

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 as a particular case. Moreover, we answer positively to one of the questions raised by Mattila in the same paper.

19 pages; [v2] minor changes for publication

References in corpus (2)

• Q-valued functions revisited
• Higher integrability and approximation of minimal currents

Cited by in corpus (2)

• Multiple valued Jacobi fields
• Partial Hölder continuity for Q-valued energy minimizing maps