Castaing, Charles; Raynaud de Fitte, Paul; Salvadori, Anna Some variational convergence results for a class of evolution inclusions of second order using Young measure. (English) Zbl 1145.49005 Kusuoka, S. (ed.) et al., Advances in mathematical economics. Vol. 7. Tokyo: Springer (ISBN 978-4-431-24332-8/hbk). Advances in Mathematical Economics 7, 1-32 (2005). Summary: This paper has two main parts. In the first part, we discuss the existence and uniqueness of a \(W_E^{2,1}\)-solution \(u_{\mu,\nu}\) of a second-order differential equation with two boundary points conditions in a finite dimensional space, governed by controls \(\mu,\nu\) which are measures on a compact metric space. We also discuss the dependence on the controls and the variational properties of the value function \(V_h(t,\mu):= \sup_{\mu\in{\mathcal R}} h(u_{\mu,\nu}(t))\), 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 \(\nu\) and we show that the limit measure \(\nu\) satisfies a Fatou-type lemma in mathematical economics with variational-type inclusion property.For the entire collection see [Zbl 1142.91009]. Cited in 1 Document MSC: 49J40 Variational inequalities 49J45 Methods involving semicontinuity and convergence; relaxation 46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics 34G25 Evolution inclusions Keywords:Fatou lemma; value function; second-order differential equation; second-order differential inclusion; Young measure; fiber product PDFBibTeX XMLCite \textit{C. Castaing} et al., Adv. Math. Econ. 7, 1--32 (2005; Zbl 1145.49005)