Γ‐convergence for one‐dimensional Ginzburg‐Landau functional with generalized Lipschitz penalizing term
Andrija Raguž · PAMM · 2010
Abstract We use the approach developed in the paper G. Alberti, S. Muller: A new approach to variational problems with multiple scales, Comm. Pure Appl. Math. 54, 761‐825 (2001) to obtain Γ‐convergence for a class of Ginzburg‐Landau functionals Iε(v), where v = v(s) is appropriate Sobolev function. 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 = g(s). In this note we prove Γ‐convergence when g = g(s, v(s), v′(s)) under suitable growth conditions imposed on g. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)