Sparse optimal control of a quasilinear elliptic PDE in measure spaces
Fabian Hoppe, Institut für Numerische Simulation, Rheinische Friedrich-Wilhelms-Universität Bonn, Friedrich-Hirzebruch-Allee 7, 53115 Bonn, Germany · Mathematical Control and Related Fields · 2022
We prove existence of optimal controls for sparse optimal control of a quasilinear elliptic equation in measure spaces and derive first-order necessary optimality conditions. Under additional assumptions also second-order necessary and sufficient optimality conditions are obtained.