Abstract
In this paper, we present a method of deriving majorants of the difference between exact solutions of elliptic type variational inequalities and functions lying in the admissible functional class of the problem under consideration. We analyze three classical problems associated with stationary variational inequalities: the problem with two obstacles, the elastoplastic torsion problem and the problem with friction type boundary conditions. The majorants are obtained by a modification of the duality technique earlier used by the author for variational problems with uniformly convex functionals. These majorants naturally reflects properties of exact solutions and possess necessary continuity conditions. Bibliography: 15 titles.
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Repin, S.I. Estimates of Deviations from Exact Solutions of Elliptic Variational Inequalities. Journal of Mathematical Sciences 115, 2811–2819 (2003). https://doi.org/10.1023/A:1023378021130
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DOI: https://doi.org/10.1023/A:1023378021130