Singular perturbations as a selection criterion for periodic minimizing sequences

  • Stefan Müller


Minimizers of functionals like\(\int_0^1 { \in ^2 u^2 _{xx} } + (u_x^2 - 1)^2 + u^2 dx\) subject to periodic (or Dirichlet) boundary conditions are investigated. While for ε=0 the infimum is not attained it is shown that for sufficiently small ε > 0, all minimizers are periodic with period ∼ ε1/3. Connections with solid-solid phase transformations are indicated.

Mathematics subject classification

34E15 49J45 (34C25, 35M10) 


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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Stefan Müller
    • 1
  1. 1.Institut für Angewandte MathematikUniversität BonnBonn 1Germany

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