Some variational convergence results for a class of evolution inclusions of second order using Young measures.

This paper has two main parts. In the first part, we discuss the existence and uniqueness of the WE2,1-solution uμ,ν of a second order differential equation with two boundary points conditions in a finite dimensional space, governed by controls μ, ν which are measures on a compact metric space. We also discuss the dependence on the controls and the variational properties of the value function Vh(t, μ) := supν∈ℜh(uμ, ν(t)), associated with a bounded lower semicontinuous function h. In the second main part, we discuss the limiting behaviour of a sequence of dynamics governed by second order evolution inclusions with two boundary points conditions. We prove that (up to extracted sequences) the solutions stably converge to a Young measure ν and we show that the limit measure ν satisfies a Fatou-type lemma in Mathematical Economics with variational-type inclusion property. [ABSTRACT FROM AUTHOR]