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Some Remarks on Separately Convex Functions

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Microstructure and Phase Transition

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 54))

Abstract

I want to discuss here some results concerning separately convex functions. Most of these results were obtained some time ago but only mentioned to a few specialists, and I had not taken the time to publish them before, for obvious reasons. The motivation of these studies was nonlinear elasticity, but once I had solved an academic example where quasiconvexity had been replaced by separate convexity, it was not clear to me how to get further on. I find useful to choose this subject now in order to describe the evolution of some ideas during the last fifteen years.

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References

  1. John M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch.Rat. Mach. Anal., 63 (1977), pp. 337–403.

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  2. John M. Ball Fran&Cois Murat, Remarks on rank-one convexity and quasiconvexity, Proceedings, Dundee, July 1990 (to appear).

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  3. Kaushik Bhattacharya Nick Firoozye &Richard James & Robert V. Kohn, Restrictions on microstructures

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  4. David Kinderlehrer &Pablo Pedregal, Characterizations of gradient Young measures

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  5. Luc Tartar, Compensated compactness and applications to partial differential equations, in Nonlinear Analysis and Mechanics: Heriot-Watt Symposium IV, Pitman Research Notes in Mathematics 39, 1979, pp. 136–212.

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Author information

Authors and Affiliations

  1. Carnegie-Mellon University, USA

    Luc Tartar

Authors
  1. Luc Tartar
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    David Kinderlehrer

  2. Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN, 55455, USA

    Richard James

  3. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Mitchell Luskin

  4. 5378 Buckskin Bob Drive, Florence, OR, 97439, USA

    Jerry L. Ericksen

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© 1993 Springer-Verlag New York, Inc.

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Tartar, L. (1993). Some Remarks on Separately Convex Functions. In: Kinderlehrer, D., James, R., Luskin, M., Ericksen, J.L. (eds) Microstructure and Phase Transition. The IMA Volumes in Mathematics and its Applications, vol 54. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8360-4_12

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  • DOI: https://doi.org/10.1007/978-1-4613-8360-4_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8362-8

  • Online ISBN: 978-1-4613-8360-4

  • eBook Packages: Springer Book Archive

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