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Nonconvexity and Microstructure

  • Sören BartelsEmail author
Chapter
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 47)

Abstract

Infinite-dimensional minimization problems without convexity properties may lead to the nonexistence of solutions, but arise as simplified mathematical descriptions of crystalline phase transitions that enable the shape-memory effect of smart materials. The ill-posed minimization problems capture important effects and relaxation theories define well-posed modifications of the functionals. The problems related to direct numerical treatment of the original formulations and the convergence and numerical solution of discretizations of its modifications are investigated in this chapter.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Abteilung für Angewandte MathematikAlbert-Ludwigs-Universität FreiburgFreiburgGermany

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