Semicontinuité pour des intégrandes polyconvexes sans continuité des déterminants. (Semicontinuity for polyconvex integrands without continuity of determinants). (French) Zbl 0723.49007

Dacorogna, Bernard; Marcellini, Paolo

C. R. Acad. Sci., Paris, Sér. I 311, No. 6, 393-396 (1990).

Summary: To show the weak lower semicontinuity of multiple integrals of the calculus of variations, one usually proves the weak continuity of all the minors of the gradient matrix. We show that in some cases one can obtain the weak lower semicontinuity, although the minors are not weakly continuous.

MSC:

49J45

Methods involving semicontinuity and convergence; relaxation

Keywords:

weak lower semicontinuity; multiple integrals; calculus of variations