scholarly journals Minimization of asymptotic energy of Müller's functional endowed with local nonlinear lower-order term

PAMM ◽  
2016 ◽  
Vol 16 (1) ◽  
pp. 661-662 ◽  
Author(s):  
Andrija Raguž
Keyword(s):  
Lower Order ◽  
Order Term ◽  
Lower Order Term ◽  
Asymptotic Energy

Elliptic equations with general singular lower order term and measure data

2015 ◽  
Vol 128 ◽  
pp. 391-411 ◽  
Author(s):  
Linda Maria De Cave ◽  
Francescantonio Oliva
Keyword(s):  
Lower Order ◽  
Elliptic Equations ◽  
Order Term ◽  
Lower Order Term ◽  
Measure Data

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

2014 ◽  
Vol 13 (01) ◽  
pp. 101-123 ◽  
Author(s):  
Andrija Raguž
Keyword(s):  
Asymptotic Behavior ◽  
Lower Order ◽  
Order Term ◽  
Lower Order Term ◽  
One Dimension ◽  
Young Measures ◽  
Ginzburg Landau ◽  
Carathéodory Function ◽  
Γ Convergence

We study the asymptotic behavior as ε → 0 of the Ginzburg–Landau functional [Formula: see text], 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 [Formula: see text] 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 [Formula: see text] is close to [Formula: see text], 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.

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