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Solutions of stochastic partial differential equations as extremals of convex functionals

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Summary

Stochastic evolution equations with monotone operators in Banach spaces are considered. The solutions are characterized as minimizers of certain convex functionals. The method of monotonicity is interpreted as a method of constructing minimizers to these functionals, and in this way solutions are constructed via Euler-Galerkin approximations.

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Authors and Affiliations

  1. School of Mathematics, University of Edinburgh, King's Buildings, Edinburgh, EH9 3JZ, United Kingdom

    István Gyöngy

  2. Departamento de Matemáticas, Universidad Autónoma de Madrid, Campus de Cantoblanco 28049 Madrid, Spain

    Teresa Martínez

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  1. István Gyöngy
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  2. Teresa Martínez
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Gyöngy, I., Martínez, T. Solutions of stochastic partial differential equations as extremals of convex functionals. Acta Math Hung 109, 127–145 (2005). https://doi.org/10.1007/s10474-005-0237-4

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  • DOI: https://doi.org/10.1007/s10474-005-0237-4

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