Geodesic
Existence of an optimal shape for thin rigid inclusions in the Kirchhoff--Love plate
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 4, pp. 142-151

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The paper deals with an optimal control problem for the elliptic system of equations describing an equilibrium of a Kirchhoff–Love plate with delaminated thin rigid inclusion. It is required to minimize the mean square integral deviation of the bending moment from the function given on the exterior boundary. The inclusion shape is considered as the control function. The solvability of the problem is established.
Keywords: Kirchhoff–Love plate model, thin rigid inclusion, crack, nonlinear boundary conditions, optimal control. 
@article{SJIM_2013_16_4_a12,
     author = {V. V. Shcherbakov},
     title = {Existence of an optimal shape for thin rigid inclusions in the {Kirchhoff--Love} plate},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {142--151},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2013_16_4_a12/}
}
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V. V. Shcherbakov. Existence of an optimal shape for thin rigid inclusions in the Kirchhoff--Love plate. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 4, pp. 142-151. http://geodesic.mathdoc.fr/item/SJIM_2013_16_4_a12/