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 (see ref. [10] in the bibliography) as a particular case. Moreover, we answer positively to one of the questions raised by Mattila in the same paper.
Lower semicontinuous functionals for Almgren's multiple valued functions / C. De Lellis; M. Focardi; E.N. Spadaro. - In: ANNALES ACADEMIAE SCIENTIARUM FENNICAE. MATHEMATICA. - ISSN 1239-629X. - STAMPA. - 36:(2011), pp. 393-410. [10.5186/aasfm.2011.3626]
Lower semicontinuous functionals for Almgren's multiple valued functions
FOCARDI, MATTEO;
2011
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 (see ref. [10] in the bibliography) as a particular case. Moreover, we answer positively to one of the questions raised by Mattila in the same paper.
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