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Shape and topological optimization for a fractional elliptic boundary problem | ||
| Journal of Finsler Geometry and its Applications | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 مهر 1404 اصل مقاله (349.8 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22098/jfga.2025.17676.1163 | ||
| نویسندگان | ||
| Malick FALL* 1؛ Mame Gor NGOM1؛ Guillaume Itbadio Sadio2؛ Ibrahima Faye3؛ Alassane Sy3؛ Diaraf Seck4 | ||
| 1D´epartement de Math´emtiques, Universit´e Gamal Abdel Nasser de Conakry, FST, BP 1147 Conakry, Guinea | ||
| 2Laboratoire de Math´ematiques et Applications (LMA), Universit´e Assane Seck de Ziguinchor, UFR ST BP 523 Ziguinchor, Senegal | ||
| 3Laboratoire d’Informatique, de Math´ematiques et Applications (LIMA), UFR SATIC, Universit´e Alioune Diop de Bambey, BP 30 Bambey, Senegal | ||
| 4Laboratoire de Math´ematiques de la D´ecision et d’Analyse Num´erique (L.M.D.A.N).Université Cheikh Anta Diop, Dakar, Senegal | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Shape optimization؛ shape derivative؛ optimal conditions؛ fractional laplacian | ||
| مراجع | ||
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1. G. Allaire and A. Henrot, On some recent advances in shape optimization, Comptes Rendus de l’Acad´emie des Sciences-Series IIB-Mechanics. 329 (5) (2001), 383-396. 2. T. Briancon, M. Hayouni, and M. Pierre, Lipschitz continuity of state functions in some optimal shaping, Calculus of Variations and Partial Differential Equations. 23 (1) (2005),13-32. 3. D. Bucur, G. Buttazzo, Variational methods in shape optimization problems, Progress in Nonlinear Differential Equations 65, Birkh¨auser Verlag, Basel, 2005. (Cited on p.p 212,217, 643, 650). 4. D. Bucur, G. Buttazzo, and A.Henrot, Existence results for some optimal partition problems, Advances in Mathematical Sciences and Applications. 8 (1998), 571-579. 5. G. Buttazzo and G. Dal Maso, Shape optimization for dirichlet problems: relaxed formulation and optimality conditions Applied Mathematics and Optimization. 23 (1) (1991),17-49. 6. G. Buttazzo and G. Dal Maso, An existence result for a class of shape optimization problems, Archive for Rational Mechanics and Analysis. 122 (1993), 183-195. 7. G. Buttazzo, G. Dal Maso, A. Garroni, A. Malusa, et al, On the relaxed formulation of some shape optimization problems, Advances in Mathematical Sciences and Applications.7 (1997), 1-24. 8. L. Caffarelli and L. Silvestre, An extension problem related to the fractional laplacian,Communications in partial differential equations. 32 (8) (2007), 1245-1260. 9. H. W. Alt and L. A. Caffarelli, Existence and regularity results for a minimum problem with free boundary, J. Reine Angew. Math., 325 (1981), 107-144. 10. R. Correa and A. Seeger, Directional derivative of a minimax function, Nonlinear Analysis: Theory, Methods & Applications. 9 (1) (1985), 13-22. 11. A.-L. Dalibard and D. G´erard-Varet, On shape optimization problems involving the fractional Laplacian, ESAIM: Control, Optimisation and Calculus of Variations. 19 (4)(2013), 976-1013. 12. M. C. Delfour, Differentials and semidifferentials for metric spaces of shapes and geometries, In IFIP Conference on System Modeling and Optimization. Springer, (2015),230-239. 13. M. C. Delfour, Control, shape, and topological derivatives via minimax differentiability of lagrangians, Numerical Methods for Optimal Control Problems. (2018), 137-164. 14. M. C. Delfour, Topological derivative of state-constrained objective functions: a direct method, SIAM Journal on Control and Optimization. 60 (1) (2022), 22-47. 15. M. C. Delfour and K. Sturm, Minimax differentiability via the averaged adjoint for control/shape sensitivity, IFAC-Papers OnLine. 49 (8) (2016), 142-149. 16. M. C. Delfour and J.-P. Zol´esio, Shapes and geometries: metrics, analysis, differential calculus, and optimization, SIAM. (2011). 17. E. Di Nezza, G. Palatucci, and E. Valdinoci, Hitchhiker’s guide to the fractional sobolev spaces, Bulletin des sciences math´ematiques. 136 (5) (2012), 521-573. 18. L. C. Evans, Partial differential equations, American Mathematical Society. 19 (2022). 19. M. Fall, I. Faye, A. Sy, and D. Seck, On shape optimization theory with fractional laplacian, Applied and Computational Mathematics. 10 (3) (2021), 56-68. 20. M. Fall, A. Sy, I. Faye, and D. Seck, On shape optimization theory with fractional plaplacian operators, In Abstract and Applied Analysis, volume 2025, page 1932719. 21. M. M. Fall, Regularity estimates for nonlocal schroidinger equations. arXiv:1711.02206,2017. 22. J. Fern´andez Bonder, A. Ritorto, and A. M. Salort, A class of shape optimization problems for some nonlocal operators, Advances in Calculus of Variations. 11 (4) (2018),373-386. 23. G. Gilboa and S. Osher, Nonlocal operators with applications to image processing, Multiscale Model ing & Simulation, 7 (3) (2009), 1005-1028. 24. M. Hayouni, Lipschitz continuity of the state function in a shape optimization problem,Journal of Convex Analysis. 6 (1) (1999), 71-90. 25. A. Henrot and M. Pierre, Variation et optimisation de formes: une analyse g´eom´etrique,Springer Science & Business Media. 48 (2005). 26. M. G. Ngom, I. Faye, and D. Seck, A minimax method in shape and topological derivatives and homogenization: the case of Helmholtz equation, Nonlinear Studies. 30 (1), 2023. 27. A. A. Novotny and J. Sokolowski, An introduction to the topological derivative method.Springer, 2020 28. X. Ros-Oton and J. Serra, The dirichlet problem for the fractional laplacian: regularity up to the boundary, Journal de Math´ematiques Pures et Appliqu´ees. 101 (3) (2014),275-302. 29. X. Ros-Oton and J. Serra, Boundary regularity for fully nonlinear integro-differential equations. Duke Math. J. 165 (2016), 2079-2154. 30. X. Ros-Oton and J. Serra, Regularity theory for general stable operators, Journal of Differential Equations. 260 (12) (2016), 8675-8715. 31. G. I. Sadio, A. Seck, and D. Seck, Numerical and theoretical analysis for optimal shape inverse problems, In Nonlinear Analysis, Geometry and Applications: Proceedings of the Second NLAGA BIRS Symposium, Cap Skirring, Senegal, January 25-30, 2022. Springer,(2022), 275-315. 32. V. H. Schulz, M. Siebenborn, and K. Welker, Structured inverse modeling in parabolic diffusion problems, SIAM Journal on Control and Optimization. 53 (6) (2015), 3319-3338. 33. V. H. Schulz, M. Siebenborn, and K. Welker, Towards a lagrange-newton approach for pde constrained shape optimization, New Trends in Shape Optimization. (2015), 229-249. 34. J. Sokolowski and A. Zochowski, On the topological derivative in shape optimization, SIAM journal on control and optimization. 37 (4) (1999), 1251-1272. 35. J. Sokolowski, and J.-P. Zol´esio, Introduction to shape optimization. Springer, 1992. 36. K. Sturm, Minimax lagrangian approach to the differentiability of nonlinear pde constrained shape functions without saddle point assumption, SIAM Journal on Control and Optimization. 53 (4) (2015), 2017 2039. 37. M. Warma, The fractional relative capacity and the fractional Laplacian with neumann and robin boundary conditions on open sets, Potential Analysis. 42 (2015), 499-547. | ||
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آمار تعداد مشاهده مقاله: 71 تعداد دریافت فایل اصل مقاله: 72 |
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