References
- Pólya G. Torsional rigidity, principal frequency, electrostatic capacity and symmetrization. Q Appl Math. 1948;6:267–277. doi: 10.1090/qam/26817
- Conca C, Mahadevan R, Sanz L. Shape derivative for a two-phase eigenvalue problem and optimal configuration in a ball. CANUM 2008, ESAIM Proceedings 27, EDP Sci.; Les Ulis, France; 2009. p. 311–321.
- Dambrine M, Kateb D. On the shape sensitivity of the first Dirichlet eigenvalue for two-phase problems. Appl Math Optim. 2011;63(1):45–74. doi: 10.1007/s00245-010-9111-z
- Afraites L, Dambrine M, Kateb D. Shape methods for the transmission problem with a single measurement. Numer Func Anal Opt. 2007;28:519–551. doi: 10.1080/01630560701381005
- Delfour MC, Zolésio ZP. Shapes and geometries: analysis, differential calculus, and optimization. Philadelphia: SIAM; 2001.
- Henrot A, Pierre M. Variation et optimisation de formes. Berlin: Springer Verlag; 2005. (Mathématiques & applications).
- Simon J. Second variations for domain optimization problems. Basel: Birkhauser; 1989. p. 361–378. (International series of numerical mathematics; vol. 91).
- Hiptmair R, Li J. Shape derivatives in differential forms I: an intrinsic perspective. Ann Mate Pura Appl. 2013 Feb;192(6):1077–1098. doi: 10.1007/s10231-012-0259-9
- Bandle C, Wagner A. Second domain variation for problems with Robin boundary conditions. J Optim Theory Appl. 2015;167(2):430–463. doi: 10.1007/s10957-015-0801-1
- Cavallina L. Locally optimal configurations for the two-phase torsion problem in the ball. Nonlinear Anal. 2017;162:33–48. doi: 10.1016/j.na.2017.06.005
- Novruzi A, Pierre M. Structure of shape derivatives. J Evol Equ. 2002;2:365–382. doi: 10.1007/s00028-002-8093-y