@article{10902/19202,
year = {2020},
url = {http://hdl.handle.net/10902/19202},
abstract = {An optimal control problem for a semilinear elliptic equation is discussed, where the control appears nonlinearly in the state equation but is not included in the objective functional. The existence of optimal controls is proved by a measurable selection technique. First-order necessary optimality conditions are derived and two types of second-order sufficient optimality conditions are established. A first theorem invokes a well-known assumption on the set of zeros of the switching function. A second relies on coercivity of the second derivative of the reduced objective functional. The results are applied to the convergence of optimal state functions for a finite element discretizion of the control problem.},
organization = {The first author was partially supported by the Spanish Ministerio de Economía y Competitividad under project MTM2017-83185-P.},
publisher = {Society for Industrial and Applied Mathematics},
publisher = {SIAM Journal on Control and Optimization, 2020, 58(4), 1961-1983},
title = {On optimal control problems with controls appearing nonlinearly in an elliptic state equation},
author = {Casas Rentería, Eduardo and Tröltzsch, Fredi},
}