References
Bui H. D. andEhrlacher A., “Developments of fracture mechanics in France in the last decades,” in: Fracture Research in Retrospect, Rotterdam, 1997, pp. 369–387.
Destyunder Ph. andJaoua M., “Sur une Interprétation Mathématique de l’Intégrale de Rice en Théorie de la Rupture Fragile,” Math. Meth. in the Appl. Sci.,3, 70–87 (1981).
Grisvard P., Singularities in Boundary Value Problems Recherches en Mathématiques Appliquées, Springer-Verlag, Berlin (1992).
Blat J. andMorel J. M., “Elliptic problems in image segmentation and their relation to fracture theory,” in: Recent Advances in Nonlinear Elliptic and Parabolic Problems. Proceedings of an International Conference, Longman Scientific and Technical, 1988,10, pp. 379–394.
Destyunder Ph., “Calcul de forces d’avancement d’une fissure en tenant compte du contact unilatéral entre les lèvres de la fissure,” CRAS, Sér. 2,296, 745–748 (1983).
Sokolowski J. andZolésio J. P., Introduction to Shape Optimization: Shape Sensitivity Analysis. Springer Series in Computational Mathematics, Vol. 16, Springer-Verlag, Berlin etc. (1992).
Khludnev A. M. andSokolowski J., “The Griffith formula and the Rice-Cherepanov integral for crack problems with unilateral conditions in nonsmooth domains,” European J. Appl. Math.,10, 379–394 (1999).
Khludnev A. M. andSokolowski J. “Griffith formula for elasticity system with unilateral conditions in domains with cracks,” European J. Mech., A/Solids,19, No. 1, 105–120 (2000).
Aubin J. P., Initiation à l’analyse appliquée (Foundation of applied analysis), Masson, Paris (1994).
Delfour M. C., “Shape optimization and free boundaries,” in: Proceedings of the NATO Advanced Study Institute and Séminaire de Mathématiques Supérieures, Held Montreal, Canada, June 25–July 13, 1990. NATO ASI Series. Series C. Mathematical and Physical Sciences. 380, Kluwer Academic Publishers, Dordrecht, 1992.
Delfour M. C. andZolésio J. P., “Structure of shape derivatives for nonsmooth domains,” J. Funct. Anal.,104, No. 1, 1–33 (1992).
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Nancy, France, Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 41, No. 5, pp. 1183–1203, September–October, 2000.
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Fremiot, G., Sokolowski, J. The structure theorem for the Eulerian derivative of shape functionals defined in domains with cracks. Sib Math J 41, 974–993 (2000). https://doi.org/10.1007/BF02674752
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DOI: https://doi.org/10.1007/BF02674752