- M. Dambrine, Ch. Dossal, B. Puig, A. Rondepierre

*Stochastic Differential Equations for modeling first order optimization methods.*

#### In revision

- F. Caubet, M. Dambrine and R. Mahadevan.

*Shape derivatives of eigenvalues for mixture problems. Part one : scalar problems.*

in revision in Applied Mathematics and Optimization

#### 2021

- F. Caubet, M. Dambrine and R. Mahadevan.

*Shape Derivative for Some Eigenvalue Functionals in Elasticity Theory.*

SIAM J. Control Optim., 59(2), 1218–1245.

- M.Dambrine, V. Bonnaillie-Noël, M. Dalla Riva and P. Musolino.

*Global representation and multi-scale expansion for the Dirichlet problem in a domain with a small hole close to the boundary.*

Communications in Partial Differential Equations Volume 46,Pages 282-309, 2021.

#### 2020

- M. Dambrine, B. Puig, and G. Vallet.

*A mathematical model for marine dinoflagellates blooms.*

DCDS-S Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020424

- M. Dambrine and H. Harbrecht

*Shape optimization for composite materials and scaffold structures.*

SIAM Multiscale Model. Simul., 18(2), 1136-1152, 2020.

- M. Dambrine and B. Puig

*Oriented distance point of view on random sets with application to shape optimization.*

ESAIM: Control, Optimization and Calculus of Variations, 26 (2020).

#### 2019

- M. Dambrine, H. Harbrecht and B. Puig

*Incorporating knowledge on the measurement noise in electrical impedance tomography.*

ESAIM: Control, Optimization and Calculus of Variations, 25 (2019).

- M. Dambrine and J. Lamboley.

*Stability in shape optimization with second variation.*

Journal of Differential Equations, 267(5) :3009-3045, 2019.

- F. Caubet, M. Dambrine, and H. Harbrecht.

*A new method for the data completion problem and application to obstacle detection.*

SIAM Journal on Applied Mathematics,79(1) :415-435, 2019.

#### 2018

- V. Bonnaillie-Noël, M. Dalla Riva, M. Dambrine, and P. Musolino.

*A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary.*

Journal des Mathématiques Pures et Appliquées, 116 :211-267, 2018.

#### 2017

- M. Dambrine, I. Greff, H. Harbrecht, and B. Puig.

*Numerical solution of the homogeneous Neumann boundary value problem on domains with a thin layer of random thickness.*

Journal of Computational Physics, 330 :943-959, 2017.

- M. Dambrine, H. Harbrecht, M.D. Peters, and B. Puig.

*On Bernoulli's free boundary problem with a random boundary.*

International Journal for Uncertainty Quantification, 7(4) :335-353, 2017.

#### 2016

- C. Conca, M. Dambrine, R. Mahadevan, and D. Quintero.

*Minimization of the groundstate of the mixture of two conducting materials in a small contrast regime.*

Mathematical Methods in the Applied Sciences, 39(13) :3549-3564, 2016.

- M. Dambrine and A. Laurain.

*A first order approach for worst-case shape optimization of the compliance for a mixture in the low contrast regime.*

Structural and Multidisciplinary Optimization, 54(2) :215-231, 2016.

- L. Barbet, M. Dambrine, A. Daniilidis, and L. Rifford.

*Sard theorems for Lipschitz functions and applications in optimization.*

Israel Journal of Mathematics,212(2) :757-790, 2016.

- M. Dambrine, D. Kateb, and J. Lamboley.

*An extremal eigenvalue problem for the Wentzell-Laplace operator.*

Annales de l'Institut Henri Poincare (C) Analyse Non Linéaire, 33(2) :409-450, 2016.

- V. Bonnaillie-Noël, M. Dambrine, and C. Lacave.

*Interactions between moderately close inclusions for the two-dimensional Dirichlet-Laplacian.*

Applied Mathematics Research eXpress, 2016(1) :1-23, 2016.17

- M. Dambrine, I. Greff, H. Harbrecht, and B. Puig.

*Numerical solution of the Poisson equation on domains with a thin layer of random thickness.*

SIAM Journal on Numerical Analysis, 54(2) :921-941, 2016.

#### 2015

- M. Dambrine, H. Harbrecht, and B. Puig.

*Computing quantities of interest for random domains with second order shape sensitivity analysis.*

ESAIM : Mathematical Modelling and Numerical Analysis, 49(5) :1285-1302, 2015.

- M. Dambrine, C. Dapogny, and H. Harbrecht.

*Shape optimization for quadratic functionals and states with random right-hand sides.*

SIAM Journal on Control and Optimization, 53(5) :3081-3103, 2015.

- V. Bonnaillie-Noël, M. Dambrine, F. Hérau, and G. Vial.

*Artificial conditions for the linear elasticity equations.*

Mathematics of Computation, 84(294) :1599-1632, 2015.

#### 2013

- F. Caubet, M. Dambrine, and D. Kateb.

*Shape optimization methods for the inverse obstacle problem with generalized impedance boundary conditions.*

Inverse Problems, 29(11), 2013.

- V. Bonnaillie-Noël and M. Dambrine.

*Interactions between moderately close circular inclusions : The Dirichlet-Laplace equation in the plane.*

Asymptotic Analysis, 84(3-4) :197-227, 2013.

- F. Caubet and M. Dambrine.

*Stability of critical shapes for the drag minimization problem in Stokes flow.*

Journal des Mathématiques Pures et Appliquées, 100(3) :327-346, 2013.

- L. Barbet, M. Dambrine, and A. Daniilidis.

*The Morse-Sard theorem for Clarke critical values.*

Advances in Mathematics, 242 :217-227, 2013.

- F. Caubet, M. Dambrine, D. Kateb, and C.Z. Timimoun.

*A Kohn-Vogelius formulation to detect an obstacle immersed in a fluid.*

Inverse Problems and Imaging,7(1) :123-157, 2013.

#### 2012

- F. Caubet and M. Dambrine.

*Localization of small obstacles in Stokes flow.*

InverseProblems, 28(10), 2012.

- M. Dambrine and D. Kateb.

*Persistency of wellposedness of Ventcel's boundary value problem under shape deformations.*

Journal of Mathematical Analysis and Applications, 394(1) :129-138, 2012.

- C. Amrouche, M. Dambrine, and Y. Raudin.

*An Lp theory of linear elasticity in the half-space.*

Journal of Differential Equations, 253(3) :906-932, 2012.

- J.P. Boufflet, M. Dambrine, G. Dupire, and P. Villon.

*On the necessity of Nitsche term. Part ii : An alternative approach.*

Applied Numerical Mathematics, 62(5) :521-535,2012.

- V. Bonnaillie-Noël, D. Brancherie, M. Dambrine, and G. Vial.

*Artificial boundary conditions to compute correctors in linear elasticity.*

Numerical Analysis and Applications, 5(2) :129-135, 2012.

#### 2011

- M. Badra, F. Caubet, and M. Dambrine.

*Detecting an obstacle immersed in a fluid by shape optimization methods.*

Mathematical Models and Methods in Applied Sciences,21(10) :2069-2101, 2011.

- M. Dambrine and D. Kateb.

*On the shape sensitivity of the first Dirichlet eigenvalue for two-phase problems.*

Applied Mathematics and Optimization, 63(1) :45-74, 2011.

#### 2010

- G. Dupire, J.P. Boufflet, M. Dambrine, and P. Villon.

*On the necessity of Nitsche term.*

Applied Numerical Mathematics, 60(9) :888-902, 2010.

- M. Dambrine and D. Kateb.

*On the ersatz material approximation in level-set methods.*

ESAIM - Control, Optimisation and Calculus of Variations, 16(3) :618-634,2010.

- V. Bonnaillie-Noël, M. Dambrine, F. Hérau, and G. Vial.

*On generalized Ventcel'stype boundary conditions for Laplace operator in a bounded domain.*

SIAM Journalon Mathematical Analysis, 42(2) :931-945, 2010.

- V. Bonnaillie-Noël, D. Brancherie, M. Dambrine, S. Tordeux, and G. Vial.

*Effect of micro-defects on structure failure : Coupling asymptotic analysis and strong discontinuity.*

European Journal of Computational Mechanics, 19(1-3) :165-175, 2010.

#### 2009

- V. Bonnaillie-Noël, M. Dambrine, S. Tordeux, and G. Vial.

*Interactions between moderately close inclusions for the Laplace equation.*

Mathematical Models and Methods in Applied Sciences, 19(10) :1853-1882, 2009.

#### 2008

- L. Afraites, M. Dambrine, and D. Kateb.

*On second order shape optimization methods for electrical impedance tomography.*

SIAM Journal on Control and Optimization,47(3) :1556-1590, 2008.

- M. Dambrine and D. Kateb.

*A remark on precomposition on H1/2(S1) and epsilon-identifiability of disks in tomography.*

Journal of Mathematical Analysis and Applications, 337(1) :594-616, 2008.

- D. Brancherie, M. Dambrine, G. Vial, and P. Villon.

*Effect of surface defects on structure failure : A two-scale approach.*

European Journal of Computational Mechanics,17(5-7) :613-624, 2008.

#### 2007

- L. Afraites, M. Dambrine, K. Eppler, and D. Kateb.

*Detecting perfectly insulatedobstacles by shape optimization techniques of order two.*

Discrete and Continuous Dynamical Systems - Series B, 8(2) :389-416, 2007.

- L. Afraites, M. Dambrine, and D. Kateb.

*Shape methods for the transmission problem with a single measurement.*

Numerical Functional Analysis and Optimization, 28(5-6) :519-551, 2007.

- M. Dambrine and G. Vial.

*A multiscale correction method for local singular perturbations of the boundary.*

Mathematical Modelling and Numerical Analysis, 41(1) :111-127, 2007.

- M. Dambrine and D. Kateb.

*Conformal mapping and inverse conductivity problem with one measurement.*

ESAIM - Control, Optimisation and Calculus of Variations,13(1) :163-177, 2007.

- V. Bonnaillie-Noël, M. Dambrine, S. Tordeux, and G. Vial.

*On moderately close inclusions for the Laplace equation.*

C. R. Math. Acad. Sci. Paris, 345(11) :609-614,2007.

#### 2005

- M. Dambrine and G. Vial.

*Influence of a boundary perforation on the Dirichlet energy.*

Control and Cybernetics, 34(1) :117-136, 2005.

#### 2003

- M. Dambrine, J. Sokolowski, and A. Zochowski.

*On stability analysis in shape optimisation : Critical shapes for Neumann problem.*

Control and Cybernetics, 32(3 SPEC.ISS.) :503-528, 2003..

#### 2002

- Marc Dambrine.

*On variations of the shape Hessian and sufficient conditions for thestability of critical shapes.*

RACSAM. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. AMat., 96(1) :95-121, 2002.

#### 2000

- M. Dambrine and M. Pierre.

*About stability of equilibrium shapes.*

ESAIM: Mathematical Modelling and Numerical Analysis, 34(4) :811-834, 2000.