Calculus of Variations and Partial Differential Equations

, Volume 1, Issue 2, pp 169–204

Singular perturbations as a selection criterion for periodic minimizing sequences

  • Stefan Müller

DOI: 10.1007/BF01191616

Cite this article as:
Müller, S. Calc. Var (1993) 1: 169. doi:10.1007/BF01191616


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

34E1549J45(34C25, 35M10)

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

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