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Lower semicontinuity of multiple integrals and convergent integrands. (English) Zbl 0869.49010

Summary: Lower semicontinuity of multiple integrals with convergent integrands is studied. It is proved that, under certain general hypotheses such as uniform lower compactness property and locally uniformly convergence of the integrands, the lower semicontinuity of an integral functional with fixed integrands and that with a sequence of convergent integrands are equivalent. The result is applied to obtain some general lower semicontinuity theorems on multiple integrals with quasiconvex integrands, while the convergent integrands need not to be quasiconvex, which is useful in numerical approximations.

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
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