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Published in:
2011 | OriginalPaper | Chapter
Multi-Valued Variational Inequalities
Authors : Siegfried Carl, Seppo Heikkilä
Published in: Fixed Point Theory in Ordered Sets and Applications
Publisher: Springer New York
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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.