engleski

Gamma-convergence for one-dimensional Ginzburg- Landau functional with generalized Lipschitz penalizing term

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 􀀀-convergence for a class of Ginzburg- Landau functionals I"(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 􀀀- convergence when g = g(s ; v(s) ; v0(s)) under suitable growth conditions imposed on g.

Gamma-convergence, Young measures, relaxation

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