-convergence for nonlocal phase transitions
Ovidiu Savin
Mathematics Department, Columbia University, 2990 Broadway, New York, NY 10027, USAEnrico Valdinoci
Dipartimento di Matematica, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy
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Abstract
We discuss the -convergence, under the appropriate scaling, of the energy functional
with , where denotes the total contribution from in the norm of , and is a double-well potential.
When , we show that the energy -converges to the classical minimal surface functional – while, when , it is easy to see that the functional -converges to the nonlocal minimal surface functional.
Cite this article
Ovidiu Savin, Enrico Valdinoci, -convergence for nonlocal phase transitions. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 4, pp. 479–500
DOI 10.1016/J.ANIHPC.2012.01.006