@article{10902/20134,
year = {2020},
month = {10},
url = {http://hdl.handle.net/10902/20134},
abstract = {In this paper we study optimal control problems governed by a semilinear elliptic equation. The equation is nonmonotone due to the presence of a convection term, despite the monotonocity of the nonlinear term. The resulting operator is neither monotone nor coervive. However, by using conveniently a comparison principle we prove existence and uniqueness of solution for the state equation. In addition, we prove some regularity of the solution and differentiability of the relation control-to-state. This allows us to derive first and second order conditions for local optimality.},
organization = {The first two authors were partially supported by Spanish Ministerio de Economía y Competitividad under research project MTM2017-83185-P.},
publisher = {EDP Sciences},
publisher = {ESAIM: Control, Optimisation and Calculus of Variations, 2020, 26, 80},
title = {Analysis of control problems of nonmontone semilinear elliptic equations},
author = {Casas Rentería, Eduardo and Mateos Alberdi, Mariano and Rösch, Arnd},
}