Uniform estimates and limiting arguments for nonlocal minimal surfaces

Luis Caffarelli, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

114 Citations (Scopus)


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-.

Original languageEnglish
Pages (from-to)203-240
Number of pages38
JournalCalculus of Variations and Partial Differential Equations
Issue number1-2
Publication statusPublished - 1 May 2011
Externally publishedYes


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