Journal of Elasticity

, Volume 123, Issue 2, pp 225–243 | Cite as

Legendre-Hadamard Conditions for Two-Phase Configurations

  • Yury Grabovsky
  • Lev Truskinovsky


We generalize the classical Legendre-Hadamard conditions by using quadratic extensions of the energy around a set of two configurations and obtain new algebraic necessary conditions for nonsmooth strong local minimizers. The implied bounds of stability are easily accessible as we illustrate on a nontrivial example where quasiconvexification is unknown.


Martensitic phase transitions Quasiconvexity Elastic stability Ellipticity Phase boundaries Calculus of variations Strong local minimizers Laminates 

Mathematics Subject Classification

74N20 74G65 49J10 



This material is based upon work supported by the National Science Foundation under Grant No. DMS-1412058. LT was also supported by the French ANR contract EVOCRIT.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Temple UniversityPhiladelphiaUSA
  2. 2.Ecole PolytechniquePalaiseauFrance

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