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On approximation of finite-energy sequences of Muller's functional with non-standard 2-well potential

We present the basic results and conjectures regarding possibility of approximating finite- energy sequences of Müller’s functional (which was for the first time, and in its simplest form, studied in paper S. Müller: Singular perturbations as a selection criterion for periodic minimizing sequences, Calc. Var. Partial Differential Equations 1(2), 169–204 (1993)) by 1-Lipschitz and 1-periodic finite- energy sequences. Our results extend known results in the case of simplest pinning term concerning the actual minimizers as small parameter epsilon tends to zero, whereby standard assumption on growth of 2-well potential at infinity (which immediately yields equi- coercivity) is replaced by non-standard one.

Singular perturbation, Muller's functional

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