Affiliations: Dipartimento di Matematica, Università degli Studi di Pavia, Via Abbiategrasso 209, 27100 Pavia, Italy | S.I.S.S.A.-I.S.A.S., Via Beirut 2/4, 34014 Trieste, Italy
Note: [] Correspondence to: M. Amar, Dipartimento di Matematica, Università degli Studi di Pavia, Via Abbiategrasso 209, 27100 Pavia, Italy.
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′.
