Optimal control of fractional diffusion with Dirac measures

Enrique Otarola; Abner J. Salgado

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arXiv · 2608.27776

Optimal control of fractional diffusion with Dirac measures

Enrique Otarola·Abner J. Salgado

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Abstract

We study a PDE-constrained optimization problem for an elliptic equation with the spectral fractional Laplacian and a linear combination of Dirac measures as the forcing term; the controls are the amplitudes of these singular sources. We prove existence and uniqueness of an optimal solution and derive first-order optimality conditions. We then propose a discretization based on finite elements. Since the set of admissible controls is finite dimensional, the control variable itself does not require discretization. We conclude by deriving a priori error bounds

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Enrique Otarola, Abner J. Salgado. 2026-08-27. Optimal control of fractional diffusion with Dirac measures. https://arxiv.org/abs/2608.27776

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