Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 51
Number of page(s) 51
DOI https://doi.org/10.1051/cocv/2026036
Published online 15 June 2026
  1. H. Berestycki, J.-M. Roquejoffre and L. Rossi, Fisher-KPP propagation in the presence of a line: further effects. Nonlinearity 26 (2013) 2623–2640. [Google Scholar]
  2. H. Berestycki, J.-M. Roquejoffre and L. Rossi, The influence of a line with fast diffusion on Fisher-KPP propagation. J. Math. Biol. 66 (2013) 743–766. [Google Scholar]
  3. H. Berestycki, J.-M. Roquejoffre and L. Rossi, The shape of expansion induced by a line with fast diffusion in Fisher-KPP equations. Commun. Math. Phys. 343 (2016) 207–232. [Google Scholar]
  4. K. Fellner, E. Latos and B.Q. Tang, Well-posedness and exponential equilibration of a volume-surface reaction - diffusion system with nonlinear boundary coupling. Ann. l'I.H.P. Anal. Non Linéaire 35 (2018) 643–673. [Google Scholar]
  5. Y. Morita and K. Sakamoto, A diffusion model for cell polarization with interactions on the membrane. Jpn. J. Ind. Appl. Math. 35: (2018) 261–276. [Google Scholar]
  6. A. Rätz and M. Roger, Symmetry breaking in a bulk-surface reaction-diffusion model for signalling networks. Nonlinearity 27 (2014) 1805–1827. [Google Scholar]
  7. B. Bogosel, T. Giletti and A. Tellini, Propagation for kpp bulk-surface systems in a general cylindrical domain. Nonlinear Anal. 213 (2021) 112528. [Google Scholar]
  8. R.S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations. John Wiley & Sons, Chichester (2003). [Google Scholar]
  9. K.-Y. Lam and Y. Lou, Introduction to Reaction-Diffusion Equations. Theory and Applications to Spatial Ecology and Evolutionary Biology. Lect. Notes Math. Model. Life Sci. Springer, Cham (2022). [Google Scholar]
  10. L. Girardin and I. Mazari, Generalized principal eigenvalues of space-time periodic, weakly coupled, cooperative parabolic systems, Mempires de la SMF, Accepted for publication. [Google Scholar]
  11. H. Berestycki, F. Hamel and L. Roques, Analysis of the periodically fragmented environment model. I: species persistence. J. Math. Biol. 51 (2005) 75–113. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  12. T. Giletti, L. Monsaingeon and M. Zhou, A KPP road-field system with spatially periodic exchange terms. Nonlinear Anal. Theory Methods Appl. A Theory Methods 128 (2015) 273–302. [Google Scholar]
  13. I. Mazari, G. Nadin and Y. Privat, Some challenging optimization problems for logistic diffusive equations and their numerical modeling, in Numerical Control. Part A. Elsevier/North Holland, Amsterdam (2022) 401–426. [Google Scholar]
  14. J.J. Langford, Symmetrization of Poisson's equation with Neumann boundary conditions. Ann. Sci. Norm. Super. Pisa Cl. Sci. 14 (2015) 1025–1063. [Google Scholar]
  15. J.J. Langford, PDE comparison principles for Robin problems. Can. J. Math. 75 (2023) 108–139. [Google Scholar]
  16. A. Alvino, P.-L. Lions and G. Trombetti, On optimization problems with prescribed rearrangements. Nonlinear Anal. 13 (1989) 185–220. [Google Scholar]
  17. I. Mazari, G. Nadin and Y. Privat, Optimisation of the total population size for logistic diffusive equations: bang-bang property and fragmentation rate. Commun. Part. Diff. Equ. 47 (2022) 797–828. [Google Scholar]
  18. S. Cox and R. Lipton, Extremal eigenvalue problems for two-phase conductors. Arch. Rational Mech. Anal. 136 (1996) 101–117. [Google Scholar]
  19. S.J. Cox and J.R. McLaughlin, Extremal eigenvalue problems for composite membranes, I. Appl. Math. Optim. 22 (1990) 153–167. [Google Scholar]
  20. C.-Y. Kao, Y. Lou and E. Yanagida, Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains. Math. Biosci. Eng. 5 (2008) 315–335. [Google Scholar]
  21. J. Lamboley, A. Laurain, G. Nadin and Y. Privat, Properties of optimizers of the principal eigenvalue with indefinite weight and Robin conditions. Calc. Var. Part. Diff. Equ. 55 (2016). [Google Scholar]
  22. G. Talenti, Elliptic equations and rearrangements. Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 3 (1976) 697–718. [Google Scholar]
  23. G. Nadin, The effect of the Schwarz rearrangement on the periodic principal eigenvalue of a nonsymmetric operator. SIAM J. Math. Anal. 41 (2010) 2388–2406. [Google Scholar]
  24. A. Alvino, C. Nitsch and C. Trombetti, A talenti comparison result for solutions to elliptic problems with Robin boundary conditions. Commun. Pure Appl. Math. 76 (2023) 585–603. [Google Scholar]
  25. D. Chen, H. Li and Y. Wei, Comparison results for solutions of Poisson equations with Robin boundary on complete Riemannian manifolds. Int. J. Math. 34 (2023) 19. [Google Scholar]
  26. J.J. Langford and P. McDonald. Extremizing temperature functions of rods with Robin boundary conditions. Ann. Fenn. Math. 47 (2022) 759–775. [Google Scholar]
  27. A.L. Masiello and G. Paoli, Rigidity results for the p-Laplacian Poisson problem with Robin boundary conditions. J. Optim. Theory Appl. 202 (2024) 628–648. [Google Scholar]
  28. A. Mondino and M. Vedovato, A Talenti-type comparison theorem for RCD(K, N) spaces and applications. Calc. Var. Part. Diff. Equ. 60 (2021) 43. [Google Scholar]
  29. A. Celentano, C. Nitsch and C. Trombetti, On a Serrin-type overdetermined problem, Milan J. Math. 92 (2024) 579–590. [Google Scholar]
  30. B.-Z. Guo and D.-H. Yang, On convergence of boundary Hausdorff measure and application to a boundary shape optimization problem. SIAM J. Control Optim. 51 (2013) 253–272. [Google Scholar]
  31. J. Dalphin, Uniform ball property and existence of optimal shapes for a wide class of geometric functionals. Interfaces Free Bound. 20 (2018) 211–260. [Google Scholar]
  32. Y. Privat, R. Robin and M. Sigalotti, Existence of surfaces optimizing geometric and PDE shape functionals under reach constraint. Preprint, arXiv:2206.04357 [math.AP] (2022). [Google Scholar]
  33. F. Brock, An isoperimetric inequality for eigenvalues of the Stekloff problem. Z. Angew. Math. Mech. 81 (2001) 69–71. [CrossRef] [MathSciNet] [Google Scholar]
  34. J. Hersch, Quatre proprietes isoperimetriques de membranes spheriques homogenes. (Some isoperimetric properties of spherical membranes). C. R. Acad. Sci. Paris Ser. A 270 (1970) 1645–1648. [Google Scholar]
  35. M. Dambrine, D. Kateb and J. Lamboley, An extremal eigenvalue problem for the Wentzell-Laplace operator. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 33 (2016) 409–450. [Google Scholar]
  36. B. Kawohl, Rearrangements and convexity of level sets in PDE, vol. 1150 of Lect. Notes Math. Springer, Cham (1985). [Google Scholar]
  37. S. Kesavan, Symmetrization and applications, vol. 3 of Ser. Anal. World Scientific, Hackensack, NJ (2006). [Google Scholar]
  38. H. Berestycki and T. Lachand-Robert, Some properties of monotone rearrangement with applications to elliptic equations in cylinders. Math. Nachr. 266 (2004) 3–19. [Google Scholar]
  39. A. Baernstein, II, A unified approach to symmetrization, in Partial differential equations of elliptic type (Cortona, 1992), vol. XXXV of Sympos. Math.. Cambridge University Press, Cambridge (1994) 47–91. [Google Scholar]
  40. G.R. Burton, Rearrangements of functions, maximization of convex functionals, and vortex rings. Math. Ann. 276 (1987) 225–253. [CrossRef] [MathSciNet] [Google Scholar]
  41. G. Leoni, A first course in fractional Sobolev spaces, vol. 229 of Grad. Stud. Math. American Mathematical Society (AMS), Providence, RI (2023). [Google Scholar]
  42. T. Giletti, L. Monsaingeon and M. Zhou, A KPP road-field system with spatially periodic exchange terms. Nonlinear-Anal. Theory Methods Appl. Ser. A Theory Methods 128 (2015) 273–302. [Google Scholar]
  43. A. Henrot and M. Pierre, Shape Variation and Optimization, A Geometrical Analysis, vol. 28. EMS Tracts in Mathematics (2018). [Google Scholar]
  44. F. Caubet, M. Dambrine and D. Kateb, Shape optimization methods for the inverse obstacle problem with generalized impedance boundary conditions. Inverse Probi. 29 (2013) 26. [Google Scholar]
  45. I. Mazari, Quantitative inequality for the eigenvalue of a Schrödinger operator in the ball. J. Differ. Equations 269 (2020) 10181–10238. [Google Scholar]
  46. M. Dambrine and J. Lamboley, Stability in shape optimization with second variation. J. Diff. Equ. 267 (2019) 3009–3045. [Google Scholar]
  47. C. Muöller, Analysis of spherical symmetries in Euclidean spaces, vol. 129 of Appl. Math. Sci. Springer, New York, NY (1998). [Google Scholar]
  48. I. Mazari, Quantitative inequality for the eigenvalue of a Schrödinger operator in the ball. J. Diff. Equ. 269 (2020) 10181–10238. [CrossRef] [Google Scholar]
  49. M. Dambrine and D. Kateb, On the shape sensitivity of the first Dirichlet eigenvalue for two-phase problems. Appl. Math. Optim. 63 (2011) 45–74. [Google Scholar]
  50. P. Grisvard, Elliptic problems in nonsmooth domains, vol. 69 of Class. Appl. Math., reprint of the 1985 hardback edn. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2011). [Google Scholar]

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