TY - JOUR
T1 - Density estimates for a variational model driven by the Gagliardo norm
AU - Savin, Ovidiu
AU - Valdinoci, Enrico
PY - 2014/1/1
Y1 - 2014/1/1
N2 - We prove density estimates for level sets of minimizers of the energyε2s{norm of matrix}u{norm of matrix}Hs(Ω)2+∫ΩW(u)dx, with s∈(0, 1), where {norm of matrix}u{norm of matrix}Hs(Ω) denotes the total contribution from Ω in the Hs norm of u, and W is a double-well potential.As a consequence we obtain, as ε→0+, the uniform convergence of the level sets of u to either an Hs-nonlocal minimal surface if s∈(0,12), or to a classical minimal surface if s∈[12,1).
AB - We prove density estimates for level sets of minimizers of the energyε2s{norm of matrix}u{norm of matrix}Hs(Ω)2+∫ΩW(u)dx, with s∈(0, 1), where {norm of matrix}u{norm of matrix}Hs(Ω) denotes the total contribution from Ω in the Hs norm of u, and W is a double-well potential.As a consequence we obtain, as ε→0+, the uniform convergence of the level sets of u to either an Hs-nonlocal minimal surface if s∈(0,12), or to a classical minimal surface if s∈[12,1).
KW - Gagliardo norm
KW - Minimizers
KW - Variational model
UR - http://www.scopus.com/inward/record.url?scp=84888440147&partnerID=8YFLogxK
U2 - 10.1016/j.matpur.2013.05.001
DO - 10.1016/j.matpur.2013.05.001
M3 - Article
AN - SCOPUS:84888440147
SN - 0021-7824
VL - 101
SP - 1
EP - 26
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
IS - 1
ER -