Selection of minimizers for one‐dimensional Ginzburg‐Landau functional with 3‐well potential by singular lower‐order term
Andrija Raguž · PAMM · 2011
Abstract We consider a variant of the Ginzburg‐Landau type functional in one dimension with 3‐well potential, penalized by lower‐order term which has singularity in one of the zeros of the potential function. Based on 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), we obtain Gamma‐convergence and provide description of the minimizers as small parameter epsilon tends to zero. We show that introduction of singular lower‐order term results in appropriate selection of the minimizers. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)