TY - JOUR
T1 - Γ-convergence for nonlocal phase transitions
AU - Savin, Ovidiu
AU - Valdinoci, Enrico
PY - 2012/1/1
Y1 - 2012/1/1
N2 - We discuss the Γ-convergence, under the appropriate scaling, of the energy functional∥u∥Hs(Ω) 2+∫ ΩW(u)dx, with s∈(0,1), where ∥u∥Hs (Ω) denotes the total contribution from Ω in the Hs norm of u, and W is a double-well potential. When s∈[1/2,1), we show that the energy Γ-converges to the classical minimal surface functional - while, when s∈(0,1/2), it is easy to see that the functional Γ-converges to the nonlocal minimal surface functional.
AB - We discuss the Γ-convergence, under the appropriate scaling, of the energy functional∥u∥Hs(Ω) 2+∫ ΩW(u)dx, with s∈(0,1), where ∥u∥Hs (Ω) denotes the total contribution from Ω in the Hs norm of u, and W is a double-well potential. When s∈[1/2,1), we show that the energy Γ-converges to the classical minimal surface functional - while, when s∈(0,1/2), it is easy to see that the functional Γ-converges to the nonlocal minimal surface functional.
UR - http://www.scopus.com/inward/record.url?scp=84864122662&partnerID=8YFLogxK
U2 - 10.1016/j.anihpc.2012.01.006
DO - 10.1016/j.anihpc.2012.01.006
M3 - Article
AN - SCOPUS:84864122662
VL - 29
SP - 479
EP - 500
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
SN - 0294-1449
IS - 4
ER -