Local minimisers and singular perturbations

@article{Kohn1989LocalMA,
  title={Local minimisers and singular perturbations},
  author={Robert V. Kohn and Peter Sternberg},
  journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics},
  year={1989},
  volume={111},
  pages={69 - 84}
}
  • R. Kohn, P. Sternberg
  • Published 1989
  • Business
  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Synopsis We construct local minimisers to certain variational problems. The method is quite general and relies on the theory of Γ-convergence. The approach is demonstrated through the model problem It is shown that in certain nonconvex domains Ω ⊂ ℝn and for ε small, there exist nonconstant local minimisers uε satisfying uε ≈ ± 1 except in a thin transition layer. The location of the layer is determined through the requirement that in the limit uε →u0, the hypersurface separating the states u0… 

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