On F-convergence of quadratic functionals in the plane

摘要

In this paper, we prove that if a sequence of homeomorphisms : with S2, bounded planar domains, of Sobolev space Wioc ( R2)has uniformmly equibounded distortions in EX P (S2) and weakly converges to f in W_1~(10,c)1(Ω' R2) then the matrices A (x , f_j) of the corresponding Laplace-Beltramioperators F-converge in the Orlicz-Sobolev space W Q (0), where Q(t) = t2 log (e t), to the matrix A (x , f) of the Laplace-Beltrami operator associated to f .