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A duality theory for some non-convex functions of matrices

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Abstract

We study a special class of non-convex functions which appear in nonlinear elasticity, and we prove that they have a well-defined Legendre transform. Several examples are given, and an application to a nonlinear eigenvalue problem.

Keywords: Duality, Legendre transform, Nonlinear elasticity

Mathematics Subject Classification (2000): 05C38, 15A15, 05A15, 15A18

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Authors and Affiliations

  1. Canada Research Chair in Mathematical Economics, Pacific Institute of Mathematical Sciences, 1933 West Mall, University of British Columbia, Vancouver BC, Canada V6T 1Z2

    Ivar Ekeland

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  1. Ivar Ekeland
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Ekeland, I. A duality theory for some non-convex functions of matrices. Ricerche mat. 55, 1–12 (2006). https://doi.org/10.1007/s11587-006-0001-2

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  • DOI: https://doi.org/10.1007/s11587-006-0001-2

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