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Elements of Nonsmooth Analysis. Hemivariational Inequalities

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Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 29))

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Abstract

This chapter is devoted to the calculus developed by Clarke [9]–[14] for locally Lipschitz functions on Banach spaces, and some elements of the theory of hemivariational inequalities. We restrict ourselves to those basic elements of Clarke’s theory that are needed in the sequel. Precisely, we discuss generalized directional derivative and generalized gradient, Lebourg’s mean value theorem, chain rule, generalized gradient of integral functions and of restrictions to submanifolds. Finally, the definition of critical point in the sense of Chang [8] for a locally Lipschitz function is given and the relationship between the hemivariational inequalities and the generalized critical point problem is stressed. We close this chapter with some elements from the mathematical theory of hemivariational inequalities [33], [36], [37].

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Iasi, Romania

    D. Motreanu

  2. Department of Civil Engineering, Aristotle University, Thessaloniki, Greece

    P. D. Panagiotopoulos

  3. Faculty of Mathematics and Physics, RWTH Aachen, Germany

    P. D. Panagiotopoulos

Authors
  1. D. Motreanu
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  2. P. D. Panagiotopoulos
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© 1999 Springer Science+Business Media Dordrecht

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Motreanu, D., Panagiotopoulos, P.D. (1999). Elements of Nonsmooth Analysis. Hemivariational Inequalities. In: Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities. Nonconvex Optimization and Its Applications, vol 29. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4064-9_1

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  • DOI: https://doi.org/10.1007/978-1-4615-4064-9_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6820-5

  • Online ISBN: 978-1-4615-4064-9

  • eBook Packages: Springer Book Archive

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