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