Marc Dambrine

Research interests

I work in Applied Analysis. My main interest lays in studying the dependancy of the solution of a boundary value problem with respect to the shape of the domain. I focuss on shape optimization and asymptotic analysis.

Recently, I turn my attention to geometric uncertainties.

Publications

[41] On Bernoulli’s free boundary problem with a random boundary.
with H. Harbrecht, M. Peters and B. Puig
International Journal for Uncertainty Quantification, to appear.

[40] Numerical solution of the homogeneous Neumann boundary value problem on domains with a thin layer of random thickness.
with H. Harbrecht, I. Greff and B. Puig
Journal of Computational Physics, 54-2 (2016), pp. 921-941

[39] Numerical solution of the Poisson equation on domains with a thin layer on random thickness.
with H. Harbrecht, I. Greff and B. Puig
SIAM Numerical Analysis, 54-2 (2016), pp. 921-941

[38] A first order approach for the worst-case shape optimization of the compliance for a mixture in the low contrast regime.
with A. Laurain.
Structural and Multidisciplinary Optimization, 54 (2016), no. 2, 215-231.

[37] Minimization of the ground state of the mixture of two conducting materials in a small contrast regime.
with C. Conca, R. Mahadevan and D. Quintero.
Mathematical Methods in the Applied Sciences, 39 (2016), no. 13,3549-3564.

[36] Shape optimization for quadratic functionals and states with random right-hand sides.
with C. Dapogny and H. Harbrecht.
SIAM Control and Optimization. 53 (2015), no. 5, 3081-3103.

[35] Interactions between moderately close inclusions for the 2D Dirichlet-Laplacian.
with V. Bonnaillie-Noël and C. Lacave.
Applied Mathematics Research eXpress, 2016, no. 1, 1-23. doi:10.1093/amrx/abv008.

[34] Sard theorems for Lipschitz functions and applications in optimization.
with L. Barbet, A. Daniilidis, and L. Rifford.
Israel Journal of Mathematics, 212 (2016), no. 2, 757-790.

[33] Computing quantities of interest for random domains with second order shape sensitivity analysis.
with H. Harbrecht, and B. Puig.
ESAIM: Mathematical Modelling and Numerical Analysis. (2015) 49-5, pp. 1285-1302.

[32] An extremal eigenvalue problem for the Wentzell-Laplace operator.
with J. Lamboley and D. Kateb.
Annales de l’IHP, Analyse non linéaire, 33(2), 409-450.

[31] Artificial conditions for the linear elasticity equations.
with V. Bonnaillie-Noël, F. Hérau and G. Vial.
Math. Comp. 84 (2015), 1599-1632 .

[30] Interactions between moderately close circular inclusions: the Dirichlet-Laplace equation in the plane.
with V. Bonnaillie-Noël.
Asymptotic Analysis. 84 (2013) 197-227.

[29] Morse-Sard theorem for Clarke critical values.
with L. Barbet and A. Daniilidis.
Advances in Mathematics. (2013), 242, 217-227.

[28] Shape optimization methods for the Inverse Obstacle Problem with generalized impedance boundary conditions.
with F. Caubet and D. Kateb.
Inverse Problems. (2013) 29:115011.

[27] Stability of critical shapes for the drag minimization problem in Stokes flow.
with F. Caubet.
Journal des Mathématiques Pures et Appliquées. (2013), 100, 327-346.

[26] A Kohn-Vogelius formulation to detect an obstacle immersed in a fluid.
with F. Caubet, D. Kateb and C.Z. Timimoun.
Inverse Problems and Imaging. (2013), 7:1, 123-157.

[25] Localisation of small obstacles in Stokes flow.
with F. Caubet.
Inverse Problems. (2012), 28 :105007.

[24] A Lp theory of linear elasticity in the half-space.
with C. Amrouche and Y. Raudin.
Journal of Differential Equations. (2012), 253, 906?932.

[23] Persistency of wellposedness of Ventcel’s boundary value problem under shape deformations.
with D. Kateb.
Journal of Mathematical Analysis and Applications. (2012), 394, 129-138.

[22] On the necessity of Nitsche term. Part II: an alternative approach.
with G. Dupire, J.-P. Boufflet and P. Villon.
Applied Numerical Mathematics. (2012), 62, Vol. 5, 521-535.

[21] Artificial boundary conditions to compute correctors in linear elasticity.
with V Bonnaillie-Noël, D Brancherie, and G. Vial.
Numerical Analysis and Applications. (2012), 5, Vol. 2, 129-135.

[20] Multiscale expansion and numerical approximation for surface defects.
with V. Bonnaillie-Noël, D. Brancherie, F. Hérau, S. Tordeux and G. Vial,
ESAIM Proc. 33 (2011), p. 22-35

[19] Detecting an obstacle immersed in a fluid by shape optimization methods.
with M. Badra and F. Caubet.
M3AS: Mathematical Models and Methods in Applied Sciences. (2011), 21, Vol. 10, 20692101.

[18] On the sensitivity with respect to the shape of the first Dirichlet eigenvalue for two-phase problems.
with D. Kateb.
Applied Mathematics and Optimization. (2011), vol. 63, no. 1, 45-74.

[17] On the necessity of Nitsche term.
with G. Dupire, J.-P. Boufflet and P. Villon.
Applied Numerical Mathematics. (2010), vol. 60, no. 9, 888-902.

[16] On generalized Ventcel’s type boundary conditions for Laplace operator in a bounded domain.
with V. Bonnaillie-Noël, F. Hérau and G. Vial.
SIAM Journal of Mathematical Analysis. (2010), vol. 42, 931-945.

[15] Effect of micro-defects on structure failure : coupling asymptotic analysis and strong discontinuity approach.
with V. Bonnaillie-Noël, D. Brancherie, S. Tordeux and G. Vial.
European Journal of Computational Mechanics. (2010), vol. 19, 165-175.

[14] On the ersatz material approximation in level-set methods.
with D. Kateb.
ESAIM: Control, Optimisation and Calculus of Variations. (2010), vol. 16 , 618-634.

[13] Interactions between moderately close inclusions for the Laplace equation.
with V. Bonnaillie-Noël, S. Tordeux and G. Vial.
M3AS: Mathematical Models and Methods in Applied Sciences. (2009), vol. 19, 1853 – 1882.

[12] Effect of surface defects on structure failure: a two-scale approach.
with D. Brancherie, G. Vial and P. Villon.
European Journal of Computational Mechanics. (2008), vol. 17, no 5-7, pp. 613-624.

[11] On second order shape optimization methods for electrical impedance tomography.
with L. Afraites and D. Kateb.
SIAM Control and Optimization. (2008), vol 47-3, pp. 1556-1590.

[10] A remark on precomposition on H1/2(S1) and epsilon-identifiability of disks in tomography.
with D. Kateb.
Journal of Mathematical Analysis and Applications. (2008), vol 337, pp. 594-616.

[9] Detecting perfectly insulated obstacles by shape optimization techniques of order two.
with L. Afraites, K. Eppler and D. Kateb.
Discrete and Continuous Dynamical Systems - serie B. (2007), vol 8-2, pp. 389 - 416 ;

[8] Conformal mappings and shape derivatives for the transmission problem with a single measurement.
with L. Afraites and D. Kateb.
Numerical Functional Analysis and Optimization. (2007), vol 28- 5 & 6 , pp. 519 - 551 ;

[7] On moderately close inclusions for the Laplace equation.
with V. Bonnaillie-Noël, S. Tordeux and G. Vial.
C. R. Acad. Sci. Paris. (2007), vol. 345, num. 11, pp. 609-614.

[6] A multiscale correction method for local singular perturbations of the boundary.
with G. Vial.
ESAIM: Mathematical Modelling and Numerical Analysis. (2007) vol 41, pp. 111-128.

[5] Conformal mapping and inverse conductivity problem with one measurement.
with D. Kateb.
ESAIM: Control, Optimization and Calculus of Variations. (2007), vol 13-1, pp. 163–177.

[4] On the influence of a boundary perforation on the Dirichlet energy.
with G. Vial.
Control and cybernetics. (2005), vol. 34-1, pp. 117-136.

[3] On stability analysis in shape optimisation : critical shapes for Neumann problem.
with J. Sokolowski and A. Zochowski.
Control and cybernetics. (2003), vol 32-3, pp. 503-528.

[2] About the variations of the shape Hessian and sufficient conditions of stability for critical shapes.
Revista Real Academia Ciencias-RACSAM. (2002), vol 96-1, pp. 95-121.

[1] About stability of equilibrium shapes.
with M. Pierre.
ESAIM: Mathematical Modelling and Numerical Analysis. (2000), vol 34-4, pp. 811-834.