Naslov
Relaxation of Ginzburg-Landau functional perturbed by nonlinear lower-order term in one dimension

Autori
Raguž, Andrija

Izvornik
Analysis and Applications (0219-5305) 13 (2015), 01; 101-123

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Asymptotic analysis ; Young measures ; Ginzburg–Landau functional ; gamma convergence

Sažetak
We study the asymptotic behavior as ε → 0 of the Ginzburg–Landau functional , where A(s, v, v′) is the nonlinear lower-order term generated by certain Carathéodory function a : (0, 1)2 × R2 → R. We obtain Γ-convergence for the rescaled functionals as ε → 0 by using the notion of Young measures on micropatterns, which was introduced in 2001 by Alberti and Müller. We prove that for ε ≈ 0 the minimal value of is close to , where A∞(s) : = ½A(s, 0, -1) + ½A(s, 0, 1) and where E0 depends only on W. Further, we use this example to establish some general conclusions related to the approach of Alberti and Müller.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA