Some remarks on the convergence of solutions to elliptic equations under weak hypotheses on the data

Abstract

We study the asymptotic behavior of solutions to elliptic equations of the form (ð€€€div(Akruk) = fk in ;uk = wk on @; where Rn is a bounded open set, wk is weakly converging in H1(), fk is weakly converging in Hð€€€1(), and Ak is a sequence square matrices satisfying some uniform ellipticity and boundedness conditions, and H-converging in . In particular, we characterize the weak limits of the solutions uk and of their momenta Akruk . When Ak is symmetric and wk = w = 0, we characterize the limits of the energies for the solutions.