Issue |
ESAIM: COCV
Volume 9, February 2003
|
|
---|---|---|
Page(s) | 105 - 124 | |
DOI | https://doi.org/10.1051/cocv:2003002 | |
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; fragala@mate.polimi.it.
Received:
25
February
2002
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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