TY - JOUR
T1 - Uniform estimates and limiting arguments for nonlocal minimal surfaces
AU - Caffarelli, Luis
AU - Valdinoci, Enrico
PY - 2011/5/1
Y1 - 2011/5/1
N2 - We consider nonlocal minimal surfaces obtained by a fractional type energy functional, parameterized by s ∈ (0,1). We show that the s-energy approaches the perimeter as s → 1-. We also provide density properties and clean ball conditions, which are uniform as s → 1-, and optimal lower bounds obtained by a rearrangement result. Then, we show that s-minimal sets approach sets of minimal perimeter as s → 1-.
AB - We consider nonlocal minimal surfaces obtained by a fractional type energy functional, parameterized by s ∈ (0,1). We show that the s-energy approaches the perimeter as s → 1-. We also provide density properties and clean ball conditions, which are uniform as s → 1-, and optimal lower bounds obtained by a rearrangement result. Then, we show that s-minimal sets approach sets of minimal perimeter as s → 1-.
UR - http://www.scopus.com/inward/record.url?scp=79952985705&partnerID=8YFLogxK
U2 - 10.1007/s00526-010-0359-6
DO - 10.1007/s00526-010-0359-6
M3 - Article
AN - SCOPUS:79952985705
SN - 0944-2669
VL - 41
SP - 203
EP - 240
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 1-2
ER -