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New lower semicontinuity results for integral functionals. (English) Zbl 0642.49007

The author studies the semicontinuity of integral functionals of the type \(F(u)=\int_{\Omega}f(x,u,Du)dx\) where f is a discontinuous function of u. The techniques used are related to approximation of convex functions depending on a parameter.
Reviewer: R.Schianchi

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
26B25 Convexity of real functions of several variables, generalizations
49J20 Existence theories for optimal control problems involving partial differential equations
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