Geodesic
Difference approximations of optimization problems for semilinear elliptic equations in a convex domain with controls in the coefficients multiplying the highest derivatives
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 1, pp. 20-46 
F. V. Lubyshev; A. R. Manapova. Difference approximations of optimization problems for semilinear elliptic equations in a convex domain with controls in the coefficients multiplying the highest derivatives. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 1, pp. 20-46. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Finite difference approximations are proposed for nonlinear optimal control problems for a non-self-adjoint elliptic equation with Dirichlet boundary conditions in a convex domain $\Omega\subset\mathbb{R}^2$ with controls involved in the leading coefficients. The convergence of the approximations with respect to the state, functional, and control is analyzed, and a regularization of the approximations is proposed.

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