We study the asymptotic behavior as epsilon goes to 0 of an appropriate scaling of the following nonlocal Allen-Cahn energy,E-epsilon(s)(u) = epsilon(2s) integral integral(IxI) vertical bar u(x) - u(y)vertical bar(2)/vertical bar x - y vertical bar(1+2s) dxdy + integral(I) W(u) dx,where I is an interval in R, and W is a double-well potential. We provide a Gamma-convergence result for any s is an element of (0, 1), by extending the case when s = 1/2 studied by Alberti, Bouchitte and Seppecher in [2]. We also investigate the convergence as s NE arrow 1 of the related optimal profile problem to the local counterpart.
Gamma-Convergence for one-dimensional nonlocal phase transition energies / Palatucci, Giampiero; Vincini, Simone. - In: LE MATEMATICHE. - ISSN 0373-3505. - 75:1(2020), pp. 195-220. [10.4418/2020.75.1.10]
Gamma-Convergence for one-dimensional nonlocal phase transition energies
Palatucci, Giampiero
;Vincini, Simone
2020-01-01
Abstract
We study the asymptotic behavior as epsilon goes to 0 of an appropriate scaling of the following nonlocal Allen-Cahn energy,E-epsilon(s)(u) = epsilon(2s) integral integral(IxI) vertical bar u(x) - u(y)vertical bar(2)/vertical bar x - y vertical bar(1+2s) dxdy + integral(I) W(u) dx,where I is an interval in R, and W is a double-well potential. We provide a Gamma-convergence result for any s is an element of (0, 1), by extending the case when s = 1/2 studied by Alberti, Bouchitte and Seppecher in [2]. We also investigate the convergence as s NE arrow 1 of the related optimal profile problem to the local counterpart.File | Dimensione | Formato | |
---|---|---|---|
1982-Article Text-5948-1-10-20191224.pdf
accesso aperto
Descrizione: Palatucci-Vincini, Matematiche (2020), open access, PDF editoriale
Tipologia:
Versione (PDF) editoriale
Licenza:
Creative commons
Dimensione
217.78 kB
Formato
Adobe PDF
|
217.78 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.