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Epiconvergence of integral functionals on the space of vector measures. (English. Abridged French version) Zbl 0821.49014

A general result is presented dealing with the epi-convergence of integral functionals on the space of vector-valued measures with bounded variations defined on a Polish space and taking values in a reflexive and separable Banach space.
The result is first applied to the study of the stability of the solutions for some sweeping processes. It is proved that, under suitable assumptions, the pointwise limit of a sequence of solutions of a sequence of sweeping processes is again a solution of a sweeping process. By this result existence and uniqueness of periodic BV continuous solutions for some evolution problems governed by the sweeping process are obtained. Existence and stability of the solutions of second order sweeping processes are also obtained. Finally, an existence result for a minimum resulting from the study of second order sweeping processes is proved.

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
28B05 Vector-valued set functions, measures and integrals
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