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A theorem on lower semicontinuity of integral functionals
Published online by Cambridge University Press: 14 November 2011
Extract
A general lower semicontinuity theorem, in which not only mappings uM and PM but also the integrands fM depend on M, is proved for integrands f,fM under certain general hypotheses. These include thai f(x, u. P) is convex with respect to P and fM converge to f locally uniformly, but fM(x, u. P) are not required to be convex with respect to P and fM(x,·,·) do not even need to be lower semicontintious. Some more usable criteria for lower semicontinuity of integral funetionals are also given as corollaries of the main theorem.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 2 , 1996 , pp. 363 - 374
- Copyright
- Copyright © Royal Society of Edinburgh 1996
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