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Rigidity and gamma convergence for solid‐solid phase transitions with SO(2) invariance by Sergio Conti; Ben Schweizer is a Mathematics article available to read on EtoBox.

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## Abstract The singularly perturbed two‐well problem in the theory of solid‐solid phase transitions takes the form where __u__ : Ω ⊂ R^__n__^ → R^__n__^ is the deformation, and __W__ vanishes for all matrices in __K__ = SO(__n__)__A__ ∪ SO(__n__)__B__. We focus on the case __n__ = 2 and derive, by means of Gamma convergence, a sharp‐interface limit for __I__~ε~. The proof is based on a rigidity estimate for low‐energy functions. Our rigidity argument also gives an optimal two‐well Liouville estimate: if ∇__u__ has a small BV norm (compared to the diameter of the domain), then, in the __L__^1^ sense, either the distance of ∇__u__ from SO(2)__A__ or the one from SO(2)__B__ is controlled by the distance of ∇__u__ from __K__. This implies that the oscillation of ∇__u__ in weak __L__^1^ is controlled by the __L__^1^ norm of the distance of ∇__u__ to __K__. © 2006 Wiley Periodicals, Inc.

Who reads Rigidity and gamma convergence for solid‐solid phase transitions with SO(2) invariance?

Author

Sergio Conti; Ben Schweizer

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); John Wiley & Sons Inc.; Wiley (ISSN 0010-3640)

Published

2006

Language

EN

Field

Mathematics (Physical Sciences)