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

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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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     author = {F. V. Lubyshev and A. R. Manapova},
     title = {Difference approximations of optimization problems for semilinear elliptic equations in a convex domain with controls in the coefficients multiplying the highest derivatives},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {20--46},
     publisher = {mathdoc},
     volume = {53},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_1_a2/}
}
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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/