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Variational inequalities for the control of stochastic partial differential equations

Part of the Lecture Notes in Mathematics book series (LNM,volume 1390)

Abstract

The paper is concerned with variational inequalities arising from an optimal-stopping problem for some stochastic partial differential equations. For linear equations, the associated elliptic variational equation and inequality are formulated and studied in an L 2-setting. By introducing appropriate Gaussian Sobolev type of Hilbert spaces, existence and uniqueness theorems are proved. Variational formulation for nonlinear equations is also discussed briefly.

Keywords

  • Variational Inequality
  • Optimal Cost
  • Stochastic Partial Differential Equation
  • Wiener Space
  • Infinite Dimension

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.

This work was supported by the National Science Foundation grant DMS-87-02236.

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References

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© 1989 Springer-Verlag

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Chow, P.L., Menaldi, J.L. (1989). Variational inequalities for the control of stochastic partial differential equations. In: Da Prato, G., Tubaro, L. (eds) Stochastic Partial Differential Equations and Applications II. Lecture Notes in Mathematics, vol 1390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083935

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  • DOI: https://doi.org/10.1007/BFb0083935

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51510-4

  • Online ISBN: 978-3-540-48200-0

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