### abstract

- We construct an upper bound for the following family of functionals {E-epsilon}(epsilon > 0), which arises in the study of micromagnetics: E-epsilon(u) = integral(Omega)epsilon vertical bar del u vertical bar(2) + 1/epsilon integral(2)(R) vertical bar H-u vertical bar(2). Here Omega is a bounded domain in R-2, u is an element of H-1 (Omega, S-1) (corresponding to the magnetization) and H-u, the demagnetizing field created by u, is given by {div ((u) over tilde + H-u) = 0 in R-2, curl H-u = 0 in R-2, where (u) over tilde is the extension of u by 0 in R-2 \ Omega. Our upper bound coincides with the lower bound obtained by Riviere and Serfaty.