Lavrentiev Phenomenon in Microstructure Theory
Date
1996-08-22
Authors
Winter, Matthias
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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.</p>
<p>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.
Description
Keywords
Singular perturbation, Lavrentiev phenomenon, Martensitic phase transformation
Citation
Winter, M. (1996). Lavrentiev phenomenon in microstructure theory. <i>Electronic Journal of Differential Equations, 1996</i>(06), pp. 1-12.
Rights
Attribution 4.0 International