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 img36-quasiconvexity is introduced as a necessary and sufficient condition for (sequential) lower semicontinuity of
img8
whenever img40 is a normal integrand,img42 is open, bounded, img44 in measure, img46 inimg48 ( if img52), and img54 inimg56 (img58 if img52). Here img62 is a constant-rank partial differential operator, img64, and img66 is img36-quasiconvex if
img70
for all img72 and all img74 such thatimg76, img78, and w is Q-periodic, img84. The characterization of Young measures generated by such sequences img86 is obtained for img88, thus recovering the well known results for the framework img90 curl, i.e. when img92 for some img94, img96. In this case img36-quasiconvexity reduces to Morrey's notion of quasiconvexity.

18.10.2019, 02:10