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Journal of Elasticity

, Volume 87, Issue 1, pp 73–94 | Cite as

Qualitative Behavior of Local Minimizers of Singular Perturbed Variational Problems

  • Markus Lilli
Article

Abstract

We consider a non-convex variational problem (P) and the corresponding singular perturbed problem (P ε ). The qualitative behavior of stable critical points of (P ε ) depending on ε and a lower order term is discussed and we prove compactness of a sequence of stable critical points as ε ↘ 0. Moreover we show whether this limit is the global minimizer of (P). Furthermore uniform convergence is considered as well as the convergence rate depending on ε.

Key words

nonlinear elasticity non-convex variational problem singular perturbation stable critical point 

Mathematics Subject Classifications (2000)

34B15 34D15 74G55 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Institut für MathematikUniversität AugsburgAugsburgGermany

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