Research project around shape optimization problems

Publications and results
•   What is the optimal shape of a pipe ? A. Henrot and Y. Privat, Archive for Rational Mechanics and Analysis, Vol. 196, Issue 1 (2010), 281 - 302.
•   On the maximization of a class of functionals on convex regions, and the characterization of the farthest convex set Evans M. Harrell and A. Henrot, Mathematika, Volume 56, Issue 02  (2010), pp 245 -265.
•   On the range of the first two Dirichlet and Neumann eigenvalues of the Laplacian P.R.S. Antunes and A. Henrot, Proceedings of the Royal Society of London, Series A, June 8, 467 (2011), 1577-1603.
•   Optimal sets for a class of minimization problems with convex constraints C. Bianchini and A. Henrot, Journal of Convex Analysis, vol. 19 no 2 (2012).
•   Rebuttal of Donnelly's paper on the spectral gap M.S. Ashbaugh, A. Henrot and R.S. Laugesen, Mathematische Zeitschrift, Volume 269, Issue 1 (2011), 5-7.
•   An isoperimetric inequality for a nonlinear eigenvalue problem G. Croce, A. Henrot and G. Pisante, Annales de l'IHP, Analyse non linéaire, to appear.
•   On some spectral problems arising in dynamic populations E.H. Laamri, A. Henrot and D. Schmitt, Communications in Pure and Applied Analysis, to appear.
•   Numerical simulations for nodal domains and spectral minimal  partitions V.Bonnaillie-Noël, B. Helffer, and G. Vial, ESAIM Control Optim. Calc. Var., 16 (1) (2010) 221-246.
•   Aharonov-Bohm Hamiltonians, isospectrality and minimal partitions V.Bonnaillie-Noël, B. Helffer, and T.Hoffmann-Ostenhof, J. Phys. A, 42(18) (2009) 185203, 20.
•   Numerical analysis of nodal sets for eigenvalues of Aharonov-Bohm hamiltonians on the square and application to minimal partitions. V.Bonnaillie-Noël and B. Helffer, Experimental Mathematics, 20(3) (2011).
•   About Hölder regularity for the convex shape minimizing $\lambda_2$ J. Lamboley, Applicable analysis, Vol 90, N°2, 2011.
•   Optimal convex shapes for concave functionals D. Bucur, I. Fragalà, and J. Lamboley, COCV, to appear.
•   Regularity and singularities for optimal convex shapes in the plane J. Lamboley, A. Novruzi, and M. Pierre, submitted.
•   About local minimizers of the Mahler volume A. Henrot, E. Harrell, and J. Lamboley, Preprint.
•   Some sharp bounds for the $p$-torsion of convex polygons I. Fragalà, F. Gazzola, and J. Lamboley, Preprint.
•   Asymptotic analysis, polarization matrices and topological derivatives for piezoelectric materials with small voids G. Cardone, S.A. Nazarov and J. Sokolwski, SIAM Journal on Control and Optimization, (2010) Vol. 48, No. 6, 3925-396.
•   Shape derivative of drag functional P. I. Plotnikov and J. Sokolowski, SIAM Journal on Control and Optimization, Volume 48, Issue 7, 2010, pp. 4680-4706.
•   Singular perturbations of curved boundaries in dimension three. The spectrum of the Neumann Laplacian A. Laurain, S. Nazarov and J. Sokolowski, Journal for Analysis and its Applications, 30 (2011)2, 145-180.
•   Spectral problems in elasticity. Singular boundary perturbations S. Nazarov, J. Sokolowski, Latin American Journal of Solids and Structures, 8(2011) 27-54.
•   Locomotion and control of a self-propelled shape-changing body in a fluid T. Chambrion and A. Munnier, J. Nonlinear Sci., 1-61, 2010.
•   Detection of a moving rigid solid in a perfect fluid C. Conca, M. Malik and A. Munnier, Inverse Problems, 26 :095010, 2010.
•   Locomotion of articulated bodies in an ideal fluid : 2d model with buoyancy, circulation and collisions A. Munnier and B. Pinçon, Math. Models Methods Appl. Sci, 1899-1940, 2010.
•   Locomotion of deformables bodies in an ideal fluid : Newtonian versus Lagrangian formalisms A. Munnier, J. Nonlinear Sci., 19(6)  :665-715, 2009.
•   Shape optimization with Stokes constraints over the set of axisymmetric domains M. Bergounioux and Y. Privat, Preprint.
•   Some inverse problems around the Tokamak Tore Supra Y. Fischer, B. Marteau, and Y. Privat, Comm. Pure Appl. Anal., To appear.
•   On a Bernoulli problem with geometric constraints A. Laurain and Y. Privat, ESAIM Control Optim. Calc. Var., To appear.
•   Shape minimization of the dissipated energy in dyadic trees X. Dubois De La Sablonière, B. Mauroy and Y. Privat, Discr. Cont. Dyn. Syst. (B), Vol. 16 (3), (2011).
•   Shape optimization problems with internal constraint D. Bucur, G. Buttazzo and B. Velichkov, Preprint.
•   Shape flows for spectral optimization problems D. Bucur, G. Buttazzo and U. Stefanelli, Preprint.
•   The first biharmonic Steklov eigenvalue: the positivity preserving and shape optimization D. Bucur and F. Gazzola, Milan Journal of Mathematics, Volume 79,  1 (2011),  247--258.
•   Micro shape control, riblets and drag  minimization D. Bucur and M. Bonnivard, Submitted.
•   On the characterization of the compact embedding of Sobolev spaces D. Bucur and G. Buttazzo, Calculus of Variations and PDEs, To appear.
•   Artificial boundary conditions to compute correctors in linear elasticity V. Bonnaille-Noël, D. Brancherie, M. Dambrine and G. Vial, Numerical Analysis and Applications, 5 (2012) no. 2, 129–135.
•   Regularity and Singularities of Optimal Convex Shapes in the Plane J. Lamboley, A. Novruzi, and M. Pierre, Archive for Rational Mechanics and Analysis, Volume 205, Issue 1 (2012), Page 311-343.
•   Artificial conditions for the linear elasticity equations V. Bonnaille-Noël, M. Dambrine, F. Hérau and G. Vial, To appear in Math. of Comp., (2014).
•   Numerical methods for matching for teams and Wasserstein barycenters G. Carlier, A. Oberman, and E. Oudet, To appear in ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), (2014).
•   An extremal eigenvalue problem for the Ventcel-Laplace operator M. Dambrine, D. Kateb, and J. Lamboley, To appear in Annales IHP, (2015).
•   To appear in J. Convex Analysis On the local minimizers of the Mahler volume, (2015),

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