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

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     title = {<i>\ensuremath{\Gamma}</i>-convergence for nonlocal phase transitions},
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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://archive.numdam.org/articles/10.1016/j.anihpc.2012.01.006/

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