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We consider a shape optimization problem written in the optimal control form: the governing operator is the $p$-Laplacian in the Euclidean space $R^d$, the cost is of an integral type, and the control variable is the domain of the state equation. Conditions that guarantee the existence of an optimal domain will be discussed in various situations. It is proved that the optimal domains have a finite perimeter and, under some suitable assumptions, that they are open sets. A crucial difference is between the case $p>d$, where the existence occurs under very mild conditions, and the case $ple d$, where additional assumptions have to be made on the data.
We consider Cheeger-like shape optimization problems of the form $$minbig{|Omega|^alpha J(Omega) : Omegasubset Dbig}$$ where $D$ is a given bounded domain and $alpha$ is above the natural scaling. We show the existence of a solution and analyze as $J
We present and study novel optimal control problems motivated by the search for photovoltaic materials with high power-conversion efficiency. The material must perform the first step: convert light (photons) into electronic excitations. We formulate
In this paper, optimal actuator shape for nonlinear parabolic systems is discussed. The system under study is an abstract differential equation with a locally Lipschitz nonlinear part. A quadratic cost on the state and input of the system is consider
We consider shape optimization problems for general integral functionals of the calculus of variations that may contain a boundary term. In particular, this class includes optimization problems governed by elliptic equations with a Robin condition on
Optimal actuator design for a vibration control problem is calculated. The actuator shape is optimized according to the closed-loop performance of the resulting linear-quadratic regulator and a penalty on the actuator size. The optimal actuator shape