Gamma-convergence of quadratic functionals perturbed by bounded linear functionals

Abstract

We study the asymptotic behavior of solutions to elliptic equations of the form (􀀀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 H􀀀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.