A simplified derivation technique of topological derivatives for quasi-linear transmission problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 106.

In this paper we perform the rigorous derivation of the topological derivative for optimization problems constrained by a class of quasi-linear elliptic transmission problems. In the case of quasi-linear constraints, techniques using fundamental solutions of the differential operators cannot be applied to show convergence of the variation of the states. Some authors succeeded showing this convergence with the help of technical computations under additional requirements on the problem. Our main objective is to simplify and extend these previous results by using a Lagrangian framework and a projection trick. Besides these generalisations the purpose of this manuscript is to present a systematic derivation approach for topological derivatives.

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DOI : 10.1051/cocv/2020035
Classification : 49Q10, 49Qxx, 90C46
Mots-clés : Topological derivative, quasi-linear problems, topology optimisation, asymptotic analysis, adjoint approach 
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     author = {Gangl, Peter and Sturm, Kevin},
     title = {A simplified derivation technique of topological derivatives for quasi-linear transmission problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
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     url = {http://www.numdam.org/articles/10.1051/cocv/2020035/}
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Gangl, Peter; Sturm, Kevin. A simplified derivation technique of topological derivatives for quasi-linear transmission problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 106. doi : 10.1051/cocv/2020035. http://www.numdam.org/articles/10.1051/cocv/2020035/

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