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Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2011

Roughening instability of broken extremals

Yury Grabovsky
  • Fonction : Auteur
Lev Truskinovsky

Résumé

We derive a new general jump condition on a broken Weierstrass–Erdmann extremal of a vectorial variational problem. Such extremals, containing surfaces of gradient discontinuity, are ubiquitous in shape optimization and in the theory of elastic phase transformations. The new condition, which does not have a one dimensional analog, reflects the stationarity of the singular surface with respect to two-scale variations that are nontrivial generalizations of Weierstrass needles. The over-determinacy of the ensuing free boundary problem suggests that typical stable solutions must involve microstructures or chattering controls.

Dates et versions

hal-00655384 , version 1 (28-12-2011)

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Yury Grabovsky, Lev Truskinovsky. Roughening instability of broken extremals. Archive for Rational Mechanics and Analysis, 2011, 200, pp.183-202. ⟨10.1007/s00205-010-0377-8⟩. ⟨hal-00655384⟩
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