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On approximation of finite‐energy sequences of Müller's functional with non‐standard 2‐well potential
Author(s) -
Raguž Andrija
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710325
Subject(s) - lipschitz continuity , infinity , mathematics , term (time) , energy (signal processing) , mathematical analysis , zero (linguistics) , partial differential equation , energy functional , pure mathematics , physics , quantum mechanics , linguistics , statistics , philosophy
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. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)