Minimization of a quasi-linear Ginzburg-Landau type energy

International audienceLet G be a smooth bounded domain in R(2). Consider the functional E(epsilon) (u) = 1/2 integral(G) (p(0) + t |x|(k) |u|(t)) |del u|(2) + 1/4 epsilon(2) integral(G) (1-|u|(2))(2) on the set H(g)(1) (G, C) = {u is an element of H(1)(G, C): u = g on partial derivative G} where g is a given boundary data with degree d >= 0. In this paper we will study the behavior of minimizers u(epsilon) of E(epsilon) and we will estimate the energy E(epsilon) (u(epsilon)). (C) 2008 Elsevier Ltd. All rights reserved