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...

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Bibliographic Details
Main Authors: Emamizadeh, Behrouz, Liu, Yichen
Format: Article
Language:English
Published: 2020
Subjects:
Online Access:https://eprints.nottingham.ac.uk/59997/
Description
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.