On stability of asymptotic energy for a functional of Ginzburg‐Landau type with ε‐dependent weakly‐star convergent 1‐Lipschitz penalizing term
Andrija Raguž · PAMM · 2009
Abstract We apply the approach developed in the paper G. Alberti, S. Müller: A new approach to variational problems with multiple scales, Comm. Pure Appl. Math. 54, 761‐825 (2001) to calculate rescaled asymptotic energy associated to certain Ginzburg‐Landau functional in one dimension. We generalize results from the paper A. Raguž: Relaxation of Ginzburg‐Landau functional with 1‐Lipschitz penalizing term in one dimension by Young measures on micropatterns, Asymptotic Anal. 41(3,4), 331‐361 (2005), where original functional was penalized by 1‐Lipschitz function g. In this note we consider the case when such penalizing functions depend on small parameter ε as their derivatives oscillate with period equal to ε to the power of γ for some γ > 0. We show that there are three distinctive cases of γ which lead to different asymptotic energy. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)