Uniform estimates and limiting arguments for nonlocal minimal surfaces |
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| Authors: | Luis Caffarelli Enrico Valdinoci |
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| Affiliation: | 1. Department of Mathematics, University of Texas at Austin, 1 University Station C1200, Austin, TX, 78712-0257, USA
2. Dipartimento di Matematica, Universit?? di Roma Tor Vergata, Via della Ricerca Scientifica, 1, 00133, Rome, Italy
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| Abstract: | We consider nonlocal minimal surfaces obtained by a fractional type energy functional, parameterized by ${sin(0,1)}$ . 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?. |
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