Conti, Sergio and Dolzmann, Georg and Kirchheim, Bernd (2007) Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 24 (6). pp. 953-962. ISSN 0294-1449,
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The three-well problem consists in looking for minimizers u: Omega subset of R-3 -> R-3 of a functional I(u) = integral del W(del u)dx, where the elastic energy W models the tetragonal phase of a phase-transforming material. In particular, W attains its minimum on K = boolean OR(3)(i=1) SO(3)Ui, with Ui being the three distinct diagonal matrices with eigenvalues (lambda, lambda,(lambda) over bar), lambda, lambda > 0 and lambda not equal (lambda) over bar. We show that, for boundary values F in a suitable relatively open subset of M-3 x3 boolean AND {F: det F = det U-1}, the differential inclusion [GRAPHICS] has Lipschitz solutions. (c) 2006 Elsevier Masson SAS. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | 2-WELL PROBLEM; MICROSTRUCTURE; SEMICONTINUITY; ELASTOMERS; THEOREMS; ENERGY; differential inclusions; nonlinear elasticity; convex integration; solid-solid phase transitions |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Georg Dolzmann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 11 Jan 2021 06:11 |
| Last Modified: | 11 Jan 2021 06:11 |
| URI: | https://pred.uni-regensburg.de/id/eprint/33327 |
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