In this paper, we consider a sequence of integral functionals Fn:X→(−∞,+∞), where X is the set of those functions u belonging to W1, p(0, T), p > 1, satisfying: U(0) = A, u(T) = B. For every n∈N, Fn is represented by the sum of two integrands, where the first one is T-periodic in time and non-convex with respect to u′ and the second one depends only on u.We give a necessary and sufficient condition in order to obtain the existence of an integral functional F∞:X→(−∞,+∞) such that, for every minimizing sequence (un) converging to u∞, the lower limit of the corresponding sequence Fn(un) coincides with F∞(u∞). The integrand function in F∞ does not depend on time and, in general, it is non-convex with respect to u′. © 1994 IOS Press and the authors.
Amar, M., Cellina, A. (1994). On passing to the limit for non-convex variational problems. ASYMPTOTIC ANALYSIS, 9(2), 135-148.
On passing to the limit for non-convex variational problems
CELLINA, ARRIGO
1994
Abstract
In this paper, we consider a sequence of integral functionals Fn:X→(−∞,+∞), where X is the set of those functions u belonging to W1, p(0, T), p > 1, satisfying: U(0) = A, u(T) = B. For every n∈N, Fn is represented by the sum of two integrands, where the first one is T-periodic in time and non-convex with respect to u′ and the second one depends only on u.We give a necessary and sufficient condition in order to obtain the existence of an integral functional F∞:X→(−∞,+∞) such that, for every minimizing sequence (un) converging to u∞, the lower limit of the corresponding sequence Fn(un) coincides with F∞(u∞). The integrand function in F∞ does not depend on time and, in general, it is non-convex with respect to u′. © 1994 IOS Press and the authors.
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