Abstract
The main focus of chapters 17 is the development of dual variational formulations for multi-well optimization problems in phase-transitions. The primal formulation may not have minimizers in the classical sense. In this case, the solution through the dual formulation is a weak limit of minimizing sequences for the original problem. This chapter was published in an article form by Nonlinear Analysis-Elsevier, reference [14].
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References
F. Botelho, On duality principles for scalar and vectorial multi-well variational problems. Nonlinear Anal. 75, 1904–1918 (2012)
I.V. Chenchiah, K. Bhattacharya, The relaxation of two-well energies with possibly unequal moduli. Arch. Rational Mech. Anal. 187, 409–479 (2008)
I. Ekeland, R. Temam, Convex Analysis and Variational Problems (Elsevier-North Holland, Amsterdam 1976).
J.F. Toland, A duality principle for non-convex optimisation and the calculus of variations. Arch. Rath. Mech. Anal. 71(1), 41–61 (1979)
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Botelho, F. (2014). On Duality Principles for Scalar and Vectorial Multi-well Variational Problems. In: Functional Analysis and Applied Optimization in Banach Spaces. Springer, Cham. https://doi.org/10.1007/978-3-319-06074-3_17
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DOI: https://doi.org/10.1007/978-3-319-06074-3_17
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