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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.14940 |
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| _version_ | 1866917413726978048 |
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| author | Otarola, Enrique Salgado, Abner J. |
| author_facet | Otarola, Enrique Salgado, Abner J. |
| contents | 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 $(-Δ)^s$ with $s \in (1/2,1)$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14940 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A pointwise tracking optimal control problem for a fractional, semilinear PDE Otarola, Enrique Salgado, Abner J. Optimization and Control 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 $(-Δ)^s$ with $s \in (1/2,1)$, 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. |
| title | A pointwise tracking optimal control problem for a fractional, semilinear PDE |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.14940 |