Bump solutions for the mesoscopic Allen-Cahn equation in periodic media
نویسندگان
چکیده
Given a double-well potential F , a Z-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 −δ∆u+ F (u) δ + c0 2 Hε = 0, such that uε,R,δ goes from a δ-neighborhood of +1 in BR to a δ-neighborhood of −1 outside BR.
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