Abstract
In this chapter we present the Pontryagin type maximum principle for optimal control problems where the state equations are second order elliptic partial differential equations and variational inequalities. The existence theory of optimal controls for similar control problems can be found in Chapter 3. Unlike the evolution equations studied in the previous chapter, in this case, we do not have the time variable t. Thus, some techniques used in Chapter 4 have to be substantially modified.
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© 1995 Birkhäuser Boston
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Li, X., Yong, J. (1995). Necessary Conditions for Optimal Controls — Elliptic Partial Differential Equations. In: Optimal Control Theory for Infinite Dimensional Systems. Systems & Control: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4260-4_5
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DOI: https://doi.org/10.1007/978-1-4612-4260-4_5
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8712-4
Online ISBN: 978-1-4612-4260-4
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