Summary
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.
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Müller, S. Singular perturbations as a selection criterion for periodic minimizing sequences. Calc. Var 1, 169–204 (1993). https://doi.org/10.1007/BF01191616
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DOI: https://doi.org/10.1007/BF01191616