A pointwise tracking optimal control problem for a fractional, semilinear PDE
Optimization and Control
2026-04-17 v1
Abstract
We analyze an optimal control problem with pointwise tracking for a fractional semilinear elliptic partial differential equation. The diffusion is characterized by the spectral fractional Laplacian with , a range that guarantees the well-posedness of point evaluations of the state. In addition to the nonconvexity of the control problem, the main difficulty is that the adjoint equation is a fractional partial differential equation with a singular right-hand side: a linear combination of Dirac measures. We establish the existence of optimal solutions and derive first-order as well as necessary and sufficient second-order optimality conditions.
Cite
@article{arxiv.2604.14940,
title = {A pointwise tracking optimal control problem for a fractional, semilinear PDE},
author = {Enrique Otarola and Abner J. Salgado},
journal= {arXiv preprint arXiv:2604.14940},
year = {2026}
}