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-.
|Number of pages||38|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 1 May 2011|