Electron. J. Diff. Eqns. Vol. 1996(1996), No. 06, pp. 1-12.

Lavrentiev Phenomenon in Microstructure Theory

Matthias Winter

A variational problem arising as a model in martensitic phase transformation including surface energy is studied. It explains the complex, multi-dimensional pattern of twin branching which is often observed in a martensitic phase near the austenite interface.

We prove that a Lavrentiev phenomenon can occur if the domain is a rectangle. We show that this phenomenon disappears under arbitrarily small shears of the domain. We also prove that other perturbations of the problem lead to an extinction of the Lavrentiev phenomenon.

Submitted April 30, 1996. Published August 22, 1996.
Math Subject Classification: 49K40, 73S10.
Key Words: Singular perturbation, Lavrentiev phenomenon, martensitic phase transformation.

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Matthias Winter
Mathematisches Institut A, Universitat Stuttgart, Stuttgart, Germany
E-mail: winter@mathematik.uni-stuttgart.de
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