Analyticity of free boundary in an optimal harvesting problem
This note revisits an optimisation problem pertaining to the optimal harvesting of a marine species. The existence of solutions and the corresponding optimal conditions they satisfy have already been proved. It is known that the optimal solutions can be identified with n-dimensional shapes. We will...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/59997/ |
| Summary: | This note revisits an optimisation problem pertaining to the optimal harvesting of a marine species. The existence of solutions and the corresponding optimal conditions they satisfy have already been proved. It is known that the optimal solutions can be identified with n-dimensional shapes. We will obtain an interesting result concerning the free boundary of the optimal shapes. Indeed, we will prove that if a parameter in the admissible set is kept sufficiently small then the free boundaries will be real analytic hypersurfaces. |
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