Uniform estimates and limiting arguments for nonlocal minimal surfaces

  • Luis Caffarelli
  • Enrico ValdinociEmail author


We consider nonlocal minimal surfaces obtained by a fractional type energy functional, parameterized by \({s\in(0,1)}\). 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.

Mathematics Subject Classification (2000)

28A75 49Q05 49Q15 53A10 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA
  2. 2.Dipartimento di MatematicaUniversità di Roma Tor VergataRomeItaly

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