Abstract
This paper is devoted to optimization of so-called first-order differential (P C ) inclusions in the gradient form on a square domain. As a supplementary problem, discrete-approximation problem (P A ) is considered. In the Euler---Lagrange form, necessary and sufficient conditions are derived for the problems (P A ) and partial differential inclusions (P C ), respectively. The results obtained are based on a new concept of locally adjoint mappings. The duality theorems are proved and duality relation is established.
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