Asymptotic behavior of subfunctions of a Schr�dinger operator of finite lower order

1990 ◽  
Vol 30 (4) ◽  
pp. 626-634
Author(s):  
A. M. Russakovskii
Keyword(s):  
Asymptotic Behavior ◽  
Lower Order ◽  
Finite Lower Order

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.

scholarly journals Further results on the deficiencies of algebroid functions

1993 ◽  
Vol 47 (2) ◽  
pp. 341-346 ◽  
Author(s):  
Lianzhong Yang
Keyword(s):  
Lower Order ◽  
Algebroid Function ◽  
Algebroid Functions ◽  
Finite Lower Order

Let f(z) be an n-valued algebroid function of finite lower order μ. In this paper, we give some further results on the deficiencies of f(z). Particularly if 0 ≤ μ ≤ 1/2, the corresponding result is best possible.

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