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Reliable solutions of elliptic boundary value problems with respect to uncertain data. (English) Zbl 0896.35034
The article deals with elliptic boundary-value problems with coefficients, right-hand side, or boundary values prescribed only between certain lower and upper bounds. The author formulates a general maximization problem and proves its solvability under some conditions. An approximate finite-dimensional maximization problem is considered by means of suitable discretizations both in the space of data and in the space of state variables. Also, the convergence of solutions of the approximate maximization problems when the mesh-sizes of the discretization of both data and state variables tend to zero, is studied.

MSC:
35J20 Variational methods for second-order elliptic equations
35A35 Theoretical approximation in context of PDEs
35R60 PDEs with randomness, stochastic partial differential equations
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