Aydin, IsmailKogut, Peter2025-03-232025-03-2320242617-0108https://doi.org/10.15421/142414https://hdl.handle.net/11486/4210We study a Dirichlet optimal control problem for a quasilinear monotone elliptic equation with the so-called weighted p(x)-Laplace operator. The coefficient of the p(x)-Laplacian, the weight u, we take as a control in BV (Ω) ∩ L∞(Ω). In this article, we use box-type constraints for the admissible controls. In order to handle the inherent degeneracy of the p(x)-Laplacian, we use a special two-parametric regularization scheme. We derive existence and uniqueness of variational V -solutions to the underlying boundary value problem and the corresponding optimal control problem. Further we discuss the asymptotic behaviour of the solutions to regularized problems on each (ε, k)-level as the parameters tend to zero and infinity, respectively. The characteristic feature of the considered OCP is the fact that the exponent p(x) is assumed to be Lebesgue-measurable, and we do not impose any additional assumptions on p(x) like to be a Lipschitz function or satisfy the so-called log-Hölder continuity condition. © I. Aydin, P. Kogut, 2024.eninfo:eu-repo/semantics/openAccesscontrol in coefficientsNonlinear Dirichlet problemoptimal controlp(x)-Laplace operatorvariable exponentArticle32217520410.15421/1424142-s2.0-85211610516Q3