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. ValdinociUltimo
2013
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.
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