Given a double-well potential F, a ℤn-periodic function H, small and with zero average, and ε > 0, we find a large R, a small δ and a function Hε which is ε-close to H for which the following two problems have solutions:1. Find a set Eε,R whose boundary is uniformly close to ∂ BR and has mean curvature equal to -Hε at any point, 2. Find u = uε,R,δ solving such that uε,R,δ goes from a δ-neighborhood of +1 in BR to a δ-neighborhood of -1 outside BR.
|Number of pages||13|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 1 Jan 2011|