Lower semicontinuity of integral functionals
نویسندگان
چکیده
منابع مشابه
A Theorem on Lower Semicontinuity of Integral Functionals
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 including that f(x, u, P ) is convex respect to P and fM converge to f locally uniformly, but fM (x, u, P ) are not required to be convex respect to P and fM (x, ·, ·) do not even need to be lower semicontinuous. So...
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It is shown that the integral functional I(y,z) = J"0 f(t,y(t), z(t))dp. is lower semicontinuous on its domain with respect to the joint strong convergence of yk -» y in Lp(G) and the weak convergence of zk -» z in LAG), where 1 < p < oo and 1 < q < oo, under the following conditions. The function/: (t,x,w) -*f(t,x,w) is measurable in / for fixed (x, w), is continuous in (x, w) for a.e. /, and ...
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Let (T,r,p) be a finite measure space, X be a Banach space, P be a metric space and let L,(y,X) denote the space of equivalence classes of X-valued Bochner integrable functions on (T, T, p). We show that if $I: T x P-2x is a set-valued function such that for each fixed p E P, 4(. , p) has a measurable graph and for each fixed TV T, 4(t;) is either upper or lower semicontinuous then the Aumann i...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1974
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1974-0348582-1