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Functional a posteriori estimates for elliptic variational inequalities

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Abstract

The paper is concerned with a new way of deriving computable estimates for the difference between the exact solutions of elliptic variational inequalities and arbitrary functions in the corresponding energy space that satisfy the main (Dirichlét) boundary conditions. Unlike the method derived earlier, the estimates are obtained by certain transformations of variational inequalities without using duality arguments. For linear elliptic and parabolic problems, this method was suggested by the author in previous papers. The present paper deals with two different types of variational inequalities (also called variational inequalities of the first and second kind). The techniques discussed can be applied to other nonlinear problems related to variational inequalities. Bibliography: 20 titles.

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References

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Authors and Affiliations

  1. St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia

    S. I. Repin

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  1. S. I. Repin
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Correspondence to S. I. Repin.

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 348, 2007, pp. 147–164.

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Repin, S.I. Functional a posteriori estimates for elliptic variational inequalities. J Math Sci 152, 702–712 (2008). https://doi.org/10.1007/s10958-008-9093-4

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  • DOI: https://doi.org/10.1007/s10958-008-9093-4

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