Journal
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume 41, Issue 1-2, Pages 203-240Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00526-010-0359-6
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Funding
- NSF
- ICES
- GNAMPA
- FIRB Analysis and Beyond
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We consider nonlocal minimal surfaces obtained by a fractional type energy functional, parameterized by s is an element of (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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