GLOBAL UNIFORM ESTIMATE FOR THE MODULUS OF TWO-DIMENSIONAL GINZBURG-LANDAU VORTEXLESS SOLUTIONS WITH ASYMPTOTICALLY INFINITE BOUNDARY ENERGY

摘要

For epsilon > 0, let u(epsilon) : Omega -> R-2 be a solution of the Ginzburg-Landau system -Delta u(epsilon) = 1/epsilon(2) u(epsilon)(1 - vertical bar u(epsilon)vertical bar(2)) in a Lipschitz bounded domain Omega subset of R-2. In an energy regime that excludes interior vortices, we prove that 1- vertical bar u(epsilon)vertical bar is uniformly estimated by a positive power of epsilon globally in Omega provided that the energy of u(epsilon) at the boundary partial derivative Omega does not grow faster than epsilon(-alpha) with alpha is an element of (0,1).