A simplified derivation technique of topological derivatives for quasi-linear transmission problems

Peter Gangl, Kevin Sturm*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Article number108
Number of pages20
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume26
DOIs
Publication statusPublished - 10 Dec 2020

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