ASYMPTOTICS OF THE s-PERIMETER AS s SE arrow 0

作者：Dipierro Serena^*; Figalli Alessio; Palatucci Giampiero; Valdinoci Enrico

来源：Discrete and Continuous Dynamical Systems, 2013, 33(7): 2777-2790.

DOI：10.3934/dcds.2013.33.2777

• Nonlinear problems
• nonlocal perimeter
• fractional Laplacian
• fractional Sobolev spaces
• minimal surfaces

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.

• 出版日期2013-7