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Acta Applicandae Mathematicae

, Volume 137, Issue 1, pp 233–252 | Cite as

Minima of Invariant Functions: The Inverse Problem

  • Jürgen Scheurle
  • Sebastian Walcher
Article
  • 112 Downloads

Abstract

We determine locally minimizing functions that are invariant with respect to the action of a finite linear group. This resolves a problem which is inverse to one discussed in a seminal paper by Abud and Sartori, and occurs naturally in various physical applications, such as elasticity theory and phase transitions. A general existence result reduces the local problem to elementary computations. Some results are extended to the compact case, and some examples and applications are given.

Keywords

Symmetry breaking Orbit space Elasticity Shape-memory alloys 

Mathematics Subject Classification

13A50 58K70 74B05 74D05 

Notes

Acknowledgements

The authors gratefully acknowledge the support of the Research in Pairs program of Mathematisches Forschungsinstitut Oberwolfach (MFO) in 2012. The first author acknowledges support by the DFG-Graduiertenkolleg “Experimentelle und konstruktive Algebra” during a visit to RWTH Aachen in 2014.

The authors also thank an anonymous referee for several helpful remarks.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Zentrum MathematikTU MünchenGarchingGermany
  2. 2.Mathematik ARWTH AachenAachenGermany

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