Geodesic
A shape-topological control of variational inequalities
Eurasian mathematical journal, Tome 7 (2016) no. 3, pp. 41-52

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A shape-topological control of singularly perturbed variational inequalities is considered in the abstract framework for state-constrained optimization problems. Aiming at asymptotic analysis, singular perturbation theory is applied to the geometry-dependent objective function and results in a shape-topological derivative. This concept is illustrated analytically in a one-dimensional example problem which is controlled by an inhomogeneity posed in a domain with moving boundary. 
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     author = {V. A. Kovtunenko and G. Leugering},
     title = {A shape-topological control of variational inequalities},
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     url = {http://geodesic.mathdoc.fr/item/EMJ_2016_7_3_a5/}
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V. A. Kovtunenko; G. Leugering. A shape-topological control of variational inequalities. Eurasian mathematical journal, Tome 7 (2016) no. 3, pp. 41-52. http://geodesic.mathdoc.fr/item/EMJ_2016_7_3_a5/