Analyticity of free boundary in an optimal harvesting problem

Behrouz Emamizadeh, Yichen Liu

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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.

Original languageEnglish
Pages (from-to)1191-1199
Number of pages9
JournalLetters in Mathematical Physics
Issue number6
Publication statusPublished - 1 Jun 2020


  • Free boundary
  • Harvesting
  • Regularity
  • Semilinear equations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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