Lower semicontinuity in spaces of weakly differentiable functions

Jan Kristensen

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Submission date: 25. Jan. 1999
Pages: 53
published in: Mathematische Annalen, 313 (1999) 4, p. 653-710 
DOI number (of the published article): 10.1007/s002080050277
Bibtex
MSC-Numbers: 49J45, 28E99, 52A99
Keywords and phrases: lower semicontinuity, quasiconvexity, young measure, sobolev space with respect to a measure, gsbv
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Abstract:
Lower semicontinuity results for multiple integrals with quasiconvex integrand are obtained in the setting of Sobolev spaces with respect to a measure and in the setting of generalised special functions of bounded variation. A significant feature of the proofs is the use of Young measures.