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| Title: | Lavrentiev Phenomenon in Microstructure Theory |
| Authors: | Winter, M |
| Keywords: | Calculus of variations, Singular perturbation
Lavrentiev phenomenon, martensitic phase transformation |
| Publication Date: | 1996 |
| Publisher: | Elsevier |
| Citation: | Electronic Journal of Differential Equations 6 (1996), 1-12 |
| 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. |
| URI: | http://bura.brunel.ac.uk/handle/2438/511 |
| Appears in Collections: | Mathematics
School of Information Systems, Computing and Mathematics Research Papers
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