Publications

Preprints and submitted articles

  • Optimisation of time-space periodic eigenvalues (2025), with B. Bogosel and G. Nadin Arxiv link

  • Mean Field Games and Ideal Free Distribution (2025), with S. Cantrell, C. Cosner and A. Lam.

  • Mean-field games for harvesting problems: Uniqueness, long-time behaviour and weak KAM theory (2024), with Z. Kobeissi and D. Ruiz-Balet Arxiv link

  • Optimality conditions for the linear optimal control of non-linear equations via a Laplace type method and two-scales like expansions (2022) , with G. Nadin. Arxiv link Hal link

    • Accepted and published articles

    Please note that the published version may differ from the preprint version available. Should you need the latest version, please contact me.
    • 27-Stability of optimal shapes and convergence of thresholding algorithms in linear and spectral optimal control problems (2023), with A. Chambolle and Y. Privat.
        Accepted for publication, Mathematische Annalen.
    • 26-Another look at qualitative properties of eigenvalues using effective Hamiltonians (2024).
        Accepted for publication, Compte-rendus Mathématiques.
    • 25- Large-time optimal observation domain for linear parabolic systems (2024), with Y. Privat and E. Trélat.
        Accepted for publication, Annales de l'Institut Henri Poincaré C-Analyse non-linéaire.
    • 24-The tragedy of the commons: A Mean-Field Game approach to the reversal of travelling waves , with Z. Kobeissi and D. Ruiz-Balet
        DOI:110.1088/1361-6544/ad7b97
    • 23- Is the Faber-Krahn inequality true for the Stokes operator? , with A. Henrot and Y. Privat.
        Calculus of Variations and PDEs, 63, 228 (2024) Journal link
        DOI:10.1007/s00526-024-02820-7
    • 22- Generalized principal eigenvalues of space-time periodic, weakly coupled, cooperative, parabolic systems, with L. Girardin.
        Accepted for publication in Mémoires de la Société Mathématique de France , 2024. Arxiv preprint
    • 21-Maximising the biomass with respect to the carrying capacity: some qualitative results,
        Journal of Differential Equations, 395 (2024):238-277 Journal link
        DOI:10.1016/j.jde.2024.02.007
    • 20-Existence of optimal shapes in parabolic bilinear optimal control problems ,
        Archive for Rational Mechanics and Analysis, 248(2), 2024 Journal link
        DOI:10.1007/s00205-024-01958-0
    • 19- Analysis of a combined filtered/phase-field approach to topology optimization in elasticity , with F. Auricchio, M. Marino, U. Stefanelli.
        DOI:10.1007/s00245-024-10104-x
    • 18-The topological state derivative: an optimal control perspective on topology optimisation, with P. Baumann and K. Sturm.
        Journal of Geometric Analysis, Special Issue: Differential Geometric PDE Control, Shape Optimization and Applications, 33, 243 (2023). Journal link Arxiv link
        DOI:10.1007/s12220-023-01295-w
    • 17- The bang-bang property in some parabolic bilinear optimal control problems via two-scale asymptotic expansions .
        DOI:10.1016/j.jfa.2023.109855
    • 16-Qualitative analysis of optimisation problems with respect to non-constant Robin coefficients, with Y. Privat.
        Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, accepted for publication, 2022. Arxiv link Hal Link
    • 15- Spectral optimization of inhomogeneous plate, with E. Davoli and U. Stefanelli.
        DOI:10.1137/21M1435203
    • 14- Spatial ecology, optimal control and game theoretical fishing problems (2022) , with D. Ruiz-Balet.
        DOI:10.1007/s00285-022-01829-w
    • 13-Quantitative stability for eigenvalues of Schrodinger operator, Quantitative bathtub principle & Application to the turnpike property for a bilinear optimal control problem , With D. Ruiz-Balet.
        DOI:10.1137/21M1393121
    • 12- A note on the rearrangement of functions in time and on the parabolic Talenti inequality.
        DOI: 10.1007/s11565-022-00392-y
    • 11-Constrained control of bistable reaction-diffusion equations: Gene-flow and spatially heterogeneous models, with D. Ruiz-Balet and E. Zuazua,
        DOI:10.4171/aihpc/52
    • 10-Some comparison results and a partial bang-bang property for two-phases problems in balls.
        Mathematics in Engineering, Special Issue Calculus of Variations and Nonlinear Analysis: Advances and Applications, 2022. Journal link
        DOI:10.3934/mine.2023010
    • 9- Optimisation of the total population size for logistic diffusive equations: bang-bang property and fragmentation rate, with G. Nadin and Y. Privat.
    • 8-Shape optimization of a weighted two-phase Dirichlet eigenvalue , With G. Nadin and Y. Privat.
    • 7-Quantitative estimates for parabolic optimal control problems under $L^infty$ and $L^1$ constraints.
    • 6-Optimisation of the total population size with respect to the initial condition for semilinear parabolic equations: Two-scale expansions and symmetrisations. with G. Nadin and A. I. Toledo Marrero.
    • 5-A fragmentation phenomenon for a non-energetic optimal control problem: optimisation of the total population size in logistic diffusive models. With D. Ruiz-Balet
    • 4- Shape optimization of a Dirichlet type energy for semilinear elliptic partial differential equations. With A. Henrot and Y. Privat.
        ESAIM: Control, Optimisation and Calculus of Variations, 27 (2021) S6. Hal link Journal link
        DOI: 10.1051/cocv/2020052
    • 3- Quantitative inequality for the eigenvalue of a Schrodinger operator in the ball.
    • 2-Optimal location of resources maximizing the total population size in logistic models. With G. Nadin and Y. Privat,
        Journal de Mathématiques Pures et Appliquées , 134, (2020), pp. 1-35. Hal link Journal link.
        DOI:10.1016/j.matpur.2019.10.008.
    • 1-Trait selection and rare mutations: the case of large diffusivities ,

    Book chapters

  • Some challenging optimisation problems for logistic diffusive equations and numerical issues (2020), With G. Nadin and Y. Privat.

      • To appear in Handbook of Numerical Analysis, Volume 23, 2022 (Editors: E. Trélat, E. Zuazua). Hal link.

    Notes de cours et documents scolaires

  • Spring school in Pristina. An introduction to the calculus of variations Lecture notes (in English) for a course I taught in Pristina (Kosovo) in 2017.

  • Les théorèmes de Nash , Notes des conférences de Cédric Villani au Goutelas, parue au JME Novembre 2015. PDF .

  • De Newton à Boltzmann , Notes des conférences de Laure Saint-Raymond au Goutelas, parue au JME, Décembre 2016. PDF .

  • Equations aux dérivées partielles (Ens de Lyon, M1, 2015) , Notes du cours de T. Gallay et des TD de J. Vovelle. PDF .