Comptes Rendus
Calculus of Variations
Simple proof of two-well rigidity
Comptes Rendus. Mathématique, Volume 343 (2006) no. 5, pp. 367-370.

We give a short proof of the rigidity estimate of Müller and Chaudhuri for two strongly incompatible wells. Making strong use of the arguments of Ball and James our approach shows that incompatibility for gradient Young measures can be used to reduce rigidity estimates for several wells to one-well rigidity.

Nous donnons une démonstration simple d'une estimation de rigidité de Müller et Chaudhuri pour deux puits fortement incompatibles. Nous employons un argument de Ball et James pour montrer que l'incompatibilité pour les mesures de Young engendrées par des gradients permet de réduire les estimations de rigidité pour plusieurs puits à celles pour un puit.

Published online:
DOI: 10.1016/j.crma.2006.07.008

Camillo De Lellis 1; László Székelyhidi 2

1 Institut für Mathematik, Universität Zürich, CH-8057 Zürich
2 Departement Mathematik, ETH Zürich, CH-8092 Zürich
     author = {Camillo De Lellis and L\'aszl\'o Sz\'ekelyhidi},
     title = {Simple proof of two-well rigidity},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {367--370},
     publisher = {Elsevier},
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     number = {5},
     year = {2006},
     doi = {10.1016/j.crma.2006.07.008},
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Camillo De Lellis; László Székelyhidi. Simple proof of two-well rigidity. Comptes Rendus. Mathématique, Volume 343 (2006) no. 5, pp. 367-370. doi : 10.1016/j.crma.2006.07.008.

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[8] J.P. Matos Young measures and the absence of fine microstructures in a class of phase transitions, Eur. J. Appl. Math., Volume 3 (1992) no. 1, pp. 31-54

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