Abstract

In this article we study the asymptotic behaviour of the eigenvalues of a family of nonlinear monotone elliptic operators of the form Aε =-div(aε(x, ▽u)), which are sub-differentials of even, positively homogeneous convex functionals, under the assumption that the operators G-converge to an operator Ahom = - div(ahom(x, ▽u)). We show that any limit point λ of a sequence of eigenvalues λε is an eigenvalue of the limit operator A hom, where λε is an eigenvalue corresponding to the operator Aε. We also show the convergence of the sequence of first eigenvalues λε 1 to the corresponding first eigenvalue of the homogenized operator. © 2006 The Royal Society of Edinburgh.