# Material and Shape Derivative Method for Quasi-Linear Elliptic Systems with Applications in Inverse Electromagnetic Interface Problems

@article{Cimrk2012MaterialAS, title={Material and Shape Derivative Method for Quasi-Linear Elliptic Systems with Applications in Inverse Electromagnetic Interface Problems}, author={Ivan Cimr{\'a}k}, journal={SIAM J. Numer. Anal.}, year={2012}, volume={50}, pages={1086-1110} }

We study a shape optimization problem for quasi-linear elliptic systems. The state equations describe an interface problem and the ultimate goal of our research is to determine the interface between two materials with different physical properties. The interface is identified by the minimization of the shape (or the cost) functional representing the misfit between the data and the simulations. For shape sensitivity of the shape functional we elaborate the material and the shape derivative…

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