Electronic Journal of Differential Equations,
Vol. 1996(1996), No. 06, pp. 1-12.

Title: Lavrentiev Phenomenon in Microstructure Theory

Author: Matthias Winter (Univ. Stuttgart, Germany)

Abstract: 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.