Kurasov Singular perturbations of differential operators : Solvable Schrödinger type operators, 1999. ,
Structural optimization using topological and shape sensitivity via a level set method, Control and cybernetics, 2005. ,
Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, vol.194, issue.1, pp.363-393, 2004. ,
DOI : 10.1016/j.jcp.2003.09.032
Crack detection by the topological gradient method, Control and Cybernetics, vol.34, issue.1, pp.81-101, 2005. ,
Energy release caused by the kinking of a crack in a plane anisotropic solid, Journal of Applied Mathematics and Mechanics, vol.66, issue.3, pp.491-503, 2002. ,
DOI : 10.1016/S0021-8928(02)00059-X
Derivatives of the energy functional for 2D-problems with a crack under Signorini and friction conditions, Mathematical Methods in the Applied Sciences, vol.17, issue.6, pp.515-534, 2000. ,
DOI : 10.1016/S0997-7538(99)80022-9
Morel 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, 1988. ,
Varchon Boundary variation for a Neumann problem, Ann. Scuola Norm.Sup.Pisa Cl.Sci, vol.4, pp.29-807, 2000. ,
A Duality Approach for the Boundary Variation of Neumann Problems, SIAM Journal on Mathematical Analysis, vol.34, issue.2, pp.460-477, 2002. ,
DOI : 10.1137/S0036141002389579
Variationnal methods in some shape optimization problems, Appunti dei Corsi Tenuti da Docenti della Scuola, 2002. ,
On the Problem of Optimal Cutting, SIAM Journal on Optimization, vol.13, issue.1, pp.157-167, 2002. ,
DOI : 10.1137/S1052623401387118
Boundary optimization under pseudo curvature constraint, pp.681-699, 1996. ,
Anatomy of the shape Hessian via lie brackets, Annali di Matematica Pura ed Applicata, vol.1, issue.No. 6, pp.127-143, 1997. ,
DOI : 10.1007/BF01783465
Developements of fracture mechanics in France in the last decades, pp.369-387, 1997. ,
Doveri Continuity of Neumann linear elliptic problems on varying twodimensional bounded open sets, Commun. Partial Differ. Equations, vol.22, pp.5-6, 1997. ,
Zochowski On stability analysis in shape optimization : critical shapes for Neumann problem, 2003. ,
Zolesio Shapes and Geometries, Advances in Design and Control, Society for Industrial and Applied Mathematics (SIAM), 2001. ,
The New Family of Cracked Sets and the Image Segmentation Problem Revisited, Communications in Information and Systems, vol.4, issue.1, pp.29-52, 2004. ,
DOI : 10.4310/CIS.2004.v4.n1.a2
Sur une Interpr??tation Math??matique de l'Int??grale de Rice en Th??orie de la Rupture Fragile, Mathematical Methods in the Applied Sciences, vol.III, issue.1, pp.70-87, 1981. ,
DOI : 10.1215/S0012-7094-63-03008-4
Structure de la semi-dérivée eulérienne dans le cas de domaines fissurés et quelques applications, 2000. ,
Eulerian semiderivatives of the eigenvalues for Laplacian in domains with cracks, Adv. Math. Sci. Appl, vol.12, issue.1, pp.115-134, 2002. ,
Sokolowski A structure theorem for the Euler derivative of configuration fonctionals defined on domains with cracks Sibirsk, Mat. Zh. English translation in Siberian Math. J, vol.41, issue.5 5, pp.1183-1202, 2000. ,
Level set method for shape optimization of Signorini problem MMAR, pp.71-75, 2004. ,
Singularities in Boundary value problems, Recherches en Mathématiques appliquées .22.Paris :Masson, 1992. ,
Elliptic problems in non-smoth domains., Monographs and studies in Mathematics, 1985. ,
Sid Idris The topological asymptotic expansion for the Dirichlet Problem, pp.1042-1072, 2002. ,
Mémoire sur le problème d'analyse relatif à l'équilibre des plaques élastiques encastrées, dans Oeuvres de J, 1907. ,
Variation et optimisation de formes : une analyse géométrique, No 48 de Mathématiques et Applications, 2005. ,
DOI : 10.1007/3-540-37689-5
?ochowski Topological optimization and inverse problems Computer Assisted Mechanics and Engineering Sciences, pp.163-176, 2003. ,
Henrot On numerical solution of shape inverse problems, Computational Optimization and Applications, vol.23, issue.2, pp.231-255, 2002. ,
DOI : 10.1023/A:1020528902875
Conical differentiability for evolution variational inequalities, Journal of Differential Equations, vol.193, issue.1, pp.131-146, 2003. ,
DOI : 10.1016/S0022-0396(03)00136-0
On derivative of energy functional for elastic bodies with cracks and unilateral conditions, Quarterly of Applied Mathematics, vol.60, issue.1, pp.99-109, 2002. ,
DOI : 10.1090/qam/1878261
Sokolowski Griffith formula and Rice integral for elliptic equations with unilateral conditions in nonsmooth domains, EJAM, vol.10, pp.379-394, 1999. ,
Griffith formulae for elasticity systems with unilateral conditions in domains with cracks, European Journal of Mechanics - A/Solids, vol.19, issue.1, pp.105-119, 2000. ,
DOI : 10.1016/S0997-7538(00)00138-8
Kozlov Asymptotics of solutions near crack tips for Poisson equation with inequality type boundary conditions ,
Singular quadratic forms in perturbation theory, 1999. ,
DOI : 10.1007/978-94-011-4619-7
Computation of singular solutions in elliptic problems and elasticity, 1987. ,
The topological asymptotic, Computationnal Methods for Control Applications, International Series GAKUTO, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-01263433
Plamenevsk? Asymptotic theory of elliptic boundary value problems in singularly perturbed domains, 2000. ,
Asymptotic analysis of shape functionals, Journal de Math??matiques Pures et Appliqu??es, vol.82, issue.2, pp.125-196, 2003. ,
DOI : 10.1016/S0021-7824(03)00004-7
URL : https://hal.archives-ouvertes.fr/inria-00071952
Sokolowski The topological derivative of the Dirichlet integral due to formation of a thin ligament Siberian Math, pp.341-355, 2004. ,
Sokolowski Self adjoint extensions of differential operators in application to shape optimization Comptes Rendus Mecanique, pp.667-672, 2003. ,
Sokolowski Selfadjoint extensions for elasticity system in application to shape optimization to appear in Bulletin of the Polish Academy of, Sciences ? Mathematics ,
Sokolowski Topological derivative of the energy functional due to formation of a thin ligament on a spatial body Les prépublications de l'Institut Élie Cartan, 2004. ,
Sokolowski Self adjoint extensions for the Neumann laplacian in application to Shape Optimization, Les prépublications de l'institut Elie Cartan 9, 2003. ,
Structure of shape derivatives, Journal of Evolution Equations, vol.2, issue.3, pp.365-382, 2002. ,
DOI : 10.1007/s00028-002-8093-y
Fedkiw Level set methods and dynamic implicit surfaces, 2004. ,
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988. ,
DOI : 10.1016/0021-9991(88)90002-2
A PDE-Based Fast Local Level Set Method, Journal of Computational Physics, vol.155, issue.2, pp.410-438, 1999. ,
DOI : 10.1006/jcph.1999.6345
Soko?owski Tangent sets in Banach spaces and applications to variational inequalities Les prépublications de l'Institut Élie Cartan 42, 2000. ,
Level set methods, 1996. ,
?ochowski On the topological derivative in shape optimization, INRIA- Lorraine, 1997. ,
On the Topological Derivative in Shape Optimization, SIAM Journal on Control and Optimization, vol.37, issue.4, pp.1251-1272, 1999. ,
DOI : 10.1137/S0363012997323230
?ochowski Topological derivatives of shape functionals for elasticity systems Mechanics of Structures and Machines, pp.333-351, 2001. ,
Optimality Conditions for Simultaneous Topology and Shape Optimization, SIAM Journal on Control and Optimization, vol.42, issue.4, pp.1198-1221, 2003. ,
DOI : 10.1137/S0363012901384430
?ochowski Topological derivatives for contact problems Les prépublications de l'Institut Élie Cartan, 2003. ,
?ochowski Topological derivatives for obstacle problems Les prépublications de l'Institut Élie Cartan No, 2005. ,
Zolesio Introduction to shape optimization, 1992. ,
Second variation of energy and an associated line independent integral in fracture mechanics. II. Numerical validations, European Journal of Mechanics - A/Solids, vol.17, issue.4, pp.541-565, 1998. ,
DOI : 10.1016/S0997-7538(99)80022-9
Theory of Bessel functions Cambridge, 1944. ,
Osher A variational level set approach to multi-phase motion, J. Comp. Phys, vol.122, pp.179-195, 1996. ,