A selection lemma for sequences of measurable sets,and lower semicontinuity of multiple integrals |
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Authors: | Goswin Eisen |
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Institution: | (1) Mathematisches Institut der Universität Bonn, Wegelerstr. 10, 5300 Bonn 1 |
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Abstract: | In the present paper we show that the integral functional
is lower semicontinuous with respect to the joint convergence of yk to y in measure and the weak convergence of uk to u in L1. The integrand f: G × N × m , (x, z, p) f(x, z, p) is assumed to be measurable in x for all (z,p), continuous in z for almost all x and all p, convex in p for all (x,z), and to satisfy the condition f(x,z,p)![gE](/content/jv34q024415146t1/xxlarge8807.gif) (x) for all (x,z,p), where is some L1-function.The crucial idea of our paper is contained in the following simple |
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