ASYMPTOTICS FOR THE MINIMIZATION OF A GINZBURG-LANDAU FUNCTIONAL

Let OMEGA subset-of R2 be a smooth bounded simply connected domain. Consider the functional E(epsilon)(u) = 1/2 integral-OMEGA \delu\2 + 1/4epsilon2 integral-OMEGA (Absolute value of u2 - 1)2 on the class H(g)1 = {u is-an-element-of H-1 (OMEGA; C); u = g on partial derivative OMEGA} where g: partial derivative OMEGA --> C is a prescribed smooth map with Absolute value of g = 1 on partial derivative OMEGA and deg(g, partial derivative) = 0. Let u(epsilon) be a minimizer for E(epsilon) on H(g)1. We prove that u(epsilon) --> u0 in C1,alpha(OMEGABAR) as epsilon --> 0, where u0 is identified. Moreover \\u(epsilon) - u0\\Linfinity less-than-or-equal-to C(epsilon)2.