Volume 9, February 2003
|Page(s)||105 - 124|
|Published online||15 September 2003|
Lower semicontinuity of multiple µ-quasiconvex integrals
Dipartimento di Matematica, Politecnico di
Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy; firstname.lastname@example.org.
Lower semicontinuity results are obtained for multiple integrals of the kind , where μ is a given positive measure on , and the vector-valued function u belongs to the Sobolev space associated with μ. The proofs are essentially based on blow-up techniques, and a significant role is played therein by the concepts of tangent space and of tangent measures to μ. More precisely, for fully general μ, a notion of quasiconvexity for f along the tangent bundle to μ, turns out to be necessary for lower semicontinuity; the sufficiency of such condition is also shown, when μ belongs to a suitable class of rectifiable measures.
Mathematics Subject Classification: 28A25 / 49J45 / 26B25
Key words: Borel measures / tangent properties / lower semicontinuity.
© EDP Sciences, SMAI, 2003
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