Γ-convergence for nonlocal phase transitions
Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 4, p. 479-500

We discuss the Γ-convergence, under the appropriate scaling, of the energy functional u H s (Ω) 2 + ΩW(u)dx, with s(0,1), where u H s (Ω) denotes the total contribution from Ω in the H s norm of u, and W is a double-well potential.When s[1/2,1), we show that the energy Γ-converges to the classical minimal surface functional – while, when s(0,1/2), it is easy to see that the functional Γ-converges to the nonlocal minimal surface functional.

@article{AIHPC_2012__29_4_479_0,
     author = {Savin, Ovidiu and Valdinoci, Enrico},
     title = {$\Gamma$-convergence for nonlocal phase transitions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {29},
     number = {4},
     year = {2012},
     pages = {479-500},
     doi = {10.1016/j.anihpc.2012.01.006},
     zbl = {1253.49008},
     mrnumber = {2948285},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2012__29_4_479_0}
}
Savin, Ovidiu; Valdinoci, Enrico. Γ-convergence for nonlocal phase transitions. Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 4, pp. 479-500. doi : 10.1016/j.anihpc.2012.01.006. http://www.numdam.org/item/AIHPC_2012__29_4_479_0/

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