

Preprint 18/1998
A-quasiconvexity, lower semicontinuity and Young measures
Stefan Müller and Irene Fonseca
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Submission date: 06. Jun. 1998
Pages: 35
published in: SIAM journal on mathematical analysis, 30 (1999) 6, p. 1355-1390 (electronic)
DOI number (of the published article): 10.1137/S0036141098339885
Bibtex
MSC-Numbers: 35D99, 35E99, 49J45
Keywords and phrases: a-quasiconvexity, equi-integrability, young measure, lower semicontinuity
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Abstract:
The notion of -quasiconvexity is introduced as a necessary and sufficient condition for (sequential) lower semicontinuity of
whenever is a normal integrand,
is open, bounded,
in measure,
in
( if
), and
in
(
if
). Here
is a constant-rank partial differential operator,
, and
is
-quasiconvex if
for all and all
such that
,
, and w is Q-periodic,
. The characterization of Young measures generated by such sequences
is obtained for
, thus recovering the well known results for the framework
curl, i.e. when
for some
,
. In this case
-quasiconvexity reduces to Morrey's notion of quasiconvexity.