A theorem on lower semicontinuity of integral functionals
Zhiping Li · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1996
A general lower semicontinuity theorem, in which not only mappings u M and P M but also the integrands f M depend on M , is proved for integrands f,f M under certain general hypotheses. These include thai f(x, u. P) is convex with respect to P and f M converge to f locally uniformly, but f M (x, u. P) are not required to be convex with respect to P and f M (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.