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|Title:||Lavrentiev Phenomenon in Microstructure Theory|
|Keywords:||Calculus of variations, Singular perturbation;Lavrentiev phenomenon, martensitic phase transformation|
|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.|
|Appears in Collections:||Mathematical Science|
Dept of Mathematics Research Papers
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