Complete stickiness of nonlocal minimal surfaces for small values of the fractional parameter
Articolo
Data di Pubblicazione:
2018
Citazione:
Complete stickiness of nonlocal minimal surfaces for small values of the fractional parameter / C. Bucur, L. Lombardini, E. Valdinoci. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - (2018). [Epub ahead of print] [10.1016/j.anihpc.2018.08.003]
Abstract:
In this paper, we consider the asymptotic behavior of the fractional mean curvature when s→0+. Moreover, we deal with the behavior of s-minimal surfaces when the fractional parameter s∈(0,1) is small, in a bounded and connected open set with C2 boundary Ω⊂Rn. We classify the behavior of s-minimal surfaces with respect to the fixed exterior data (i.e. the s-minimal set fixed outside of Ω). So, for s small and depending on the data at infinity, the s-minimal set can be either empty in Ω, fill all Ω, or possibly develop a wildly oscillating boundary. Also, we prove the continuity of the fractional mean curvature in all variables, for s∈[0,1]. Using this, we see that as the parameter s varies, the fractional mean curvature may change sign.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Loss of regularity; Nonlocal minimal surfaces; Stickiness phenomena; Strongly nonlocal regime
Elenco autori:
C. Bucur, L. Lombardini, E. Valdinoci
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