We deal with the asymptotic behavior of the s-perimeter of a set E inside a domain Omega as s SE arrow 0. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of E and Omega. Moreover, we construct examples of sets for which the limit does not exist.

Asymptotics of the s-perimeter as s ↘ 0 / S. Dipierro, A. Figalli, G. Palatucci, E. Valdinoci. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 33:7(2013 Jul), pp. 2777-2790. [10.3934/dcds.2013.33.2777]

Asymptotics of the s-perimeter as s ↘ 0

S. Dipierro;E. Valdinoci
Ultimo
2013-07

Abstract

We deal with the asymptotic behavior of the s-perimeter of a set E inside a domain Omega as s SE arrow 0. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of E and Omega. Moreover, we construct examples of sets for which the limit does not exist.
nonlinear problems ; nonlocal perimeter ; fractional Laplacian ; fractional Sobolev spaces ; minimal surfaces
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/219699
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