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Control by the Right-hand Sides in Elliptic Problems

  • William G. Litvinov
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 119)

Abstract

Let U be a reflexive Banach space, and suppose
$$ \left. {\begin{array}{*{20}{c}} {u,v \to \pi (u,v)\,is\,a\,bilinear,\,symmetric,\,continuous,\; \,\,\quad \quad } \\ {positive\,form\;on\;U \times U,\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad } \\ \end{array} } \right\} $$
(3.1.1)
i.e.,
$$ \pi (u,v) = \pi (v,u)\quad \;u,v \in U, $$
$$ \left| {\pi (u,v)} \right| \leqslant c\left\| u \right\|U\left\| v \right\|U,\quad \;u,v \in U,\;\;c = const > 0, $$
$$ \pi (u,u) \geqslant 0,\quad \;u \in U $$

Keywords

Banach Space Optimal Control Problem Unique Function Elliptic Problem Weak Topology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2000

Authors and Affiliations

  • William G. Litvinov
    • 1
  1. 1.Institute of Statics and Dynamics of Aero-Space StructuresUniversity of StuttgartStuttgartDeutschland

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