On Γ-convergence of quadratic functionals in the plane

In this paper, we prove that if a sequence of homeomorphisms fjΩ → Ω , with Ω,Ω bounded planar domains, of Sobolev space W1,1locΩ, R2 has uniformly equibounded distortions in EXP(Ω) and weakly converges to f in W1,1locΩ, 2 then the matrices A(x, f j ) of the corresponding Laplace-Beltrami operators Γ-converge in the Orlicz-Sobolev space W1,QΩ), where Q(t) = t 2log(e + t), to the matrix A(x, f) of the Laplace-Beltrami operator associated to f. © 2008 Università degli Studi di Napoli "Federico II".