Multi-Valued Variational Inequalities

Siegfried Carl () and Seppo Heikkilä ()
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Siegfried Carl: Martin-Luther-Universität Halle-Wittenberg, Institut für Mathematik
Seppo Heikkilä: University of Oulu, Department of Mathematical Sciences

Chapter 3 in Fixed Point Theory in Ordered Sets and Applications, 2011, pp 57-129 from Springer

Abstract: Abstract In this chapter we provide existence, comparison, and extremality results for multi-valued elliptic and parabolic variational inequalities that will be used in subsequent chapters about discontinuously perturbed problems of this kind. The subject of this chapter is not only a prerequisite for the following chapters, but also is of independent interest. Our presentation is based on and includes results recently obtained in [38, 39, 66, 69, 70, 72], which partly generalize related results of [62] on this topic. Moreover, the theory about multi-valued elliptic and parabolic variational inequalities allows us to treat a wide range of nonsmooth elliptic and parabolic problems in a unified way.

Keywords: Variational Inequality; Auxiliary Problem; Maximal Monotone Operator; Extremal Solution; Penalty Operator (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-7585-0_3

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DOI: 10.1007/978-1-4419-7585-0_3

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