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−.

Uniform estimates and limiting arguments for nonlocal minimal surfaces / L. Caffarelli, E. Valdinoci. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 41:1-2(2011 May), pp. 203-240.

Uniform estimates and limiting arguments for nonlocal minimal surfaces

E. Valdinoci
2011

Abstract

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−.
Settore MAT/05 - Analisi Matematica
mag-2011
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/224047
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