Shape and topological optimization for a fractional elliptic boundary problem

Articles in Press

Document Type : Original Article

Authors

1 D´epartement de Math´emtiques, Universit´e Gamal Abdel Nasser de Conakry, FST, BP 1147 Conakry, Guinea

2 Laboratoire de Math´ematiques et Applications (LMA), Universit´e Assane Seck de Ziguinchor, UFR ST BP 523 Ziguinchor, Senegal

3 Laboratoire d’Informatique, de Math´ematiques et Applications (LIMA), UFR SATIC, Universit´e Alioune Diop de Bambey, BP 30 Bambey, Senegal

4 Laboratoire de Math´ematiques de la D´ecision et d’Analyse Num´erique (L.M.D.A.N).Université Cheikh Anta Diop, Dakar, Senegal

Abstract

In this paper, we consider a shape optimization problem associated with the fractional Lapla
cian We focus on J( Omega) = j( Omega,u ) where u is the solution of 1.3. We give an existence of
optimal shape using differents methods. These results are based compactness and
cone property. We establish also the shape derivative and topological derivative of the functional
using the minmax method.

Keywords

References

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Journal of Finsler Geometry and its Applications

Articles in Press, Accepted Manuscript
Available Online from 20 October 2025

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