TY - JOUR
T1 - Bump solutions for the mesoscopic Allen-Cahn equation in periodic media
AU - Novaga, Matteo
AU - Valdinoci, Enrico
PY - 2011/1/1
Y1 - 2011/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=78649904854&partnerID=8YFLogxK
U2 - 10.1007/s00526-010-0332-4
DO - 10.1007/s00526-010-0332-4
M3 - Article
AN - SCOPUS:78649904854
VL - 40
SP - 37
EP - 49
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 1
ER -