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Erratum for "Dirichlet-to-Neumann or Poincaré-Steklov operator on fractals described by $ d $-sets"

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  • We correct different points of article K. Arfi, A. Rozanova-Pierrat, Dirichlet-to-Neumann or Poincaré-Steklov operator on fractals described by $ d $-sets. Discrete & Continuous Dynamical Systems – S, Vol. 12, No. 1, 2019, pp. 1–26.

    Mathematics Subject Classification: Primary: 35P05, 35J25, 46E35; Secondary: 47A10.

    Citation:

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  • [1] R. Adams, Sobolev spaces, Pure Appl. Math., Vol. 65. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975.
    [2] W. Arendt and R. Mazzeo, Spectral properties of the Dirichlet-to-Neumann operator on Lipschitz domains, Ulmer Seminare, 12 (2007), 28-38. 
    [3] L. Bundrock, A. Girouard, D. S. Grebenkov, M. Levitin and I. Polterovich, The exterior Steklov problem for Euclidean domains, Preprint, arXiv: 2511.09490, (2025).
    [4] G. Claret, M. Hinz, A. Rozanova-Pierrat and A. Teplyaev, Layer potential operators for transmission problems on extension domains, Journal de Mathématiques Pures et Appliquées, 212 (2026), 103888, 42 pp. doi: 10.1016/j.matpur.2026.103888.
    [5] A. Dekkers and A. Rozanova-Pierrat, Dirichlet boundary valued problems for linear and nonlinear wave equations on arbitrary and fractal domains, Journal of Mathematical Analysis and Applications, 512 (2022), 126089, 45 pp. doi: 10.1016/j.jmaa.2022.126089.
    [6] A. Dekkers, A. Rozanova-Pierrat and A. Teplyaev, Mixed boundary valued problems for linear and nonlinear wave equations in domains with fractal boundaries, Calculus of Variations and Partial Differential Equations, 61 (2022), Paper No. 75, 44 pp. doi: 10.1007/s00526-021-02159-3.
    [7] M. HinzF. MagoulèsA. Rozanova-PierratM. Rynkovskaya and A. Teplyaev, On the existence of optimal shapes in architecture, Applied Mathematical Modelling, 94 (2021), 676-687.  doi: 10.1016/j.apm.2021.01.041.
    [8] F. MagoulèsT. P. Kieu NguyenP. Omnes and A. Rozanova-Pierrat, Optimal absorption of acoustic waves by a boundary, SIAM Journal on Control and Optimization, 59 (2021), 561-583.  doi: 10.1137/20M1327239.
    [9] A. Rozanova-Pierrat, Generalization of Rellich-Kondrachov theorem and trace compactness for fractal boundaries, in Fractals in Engineering: Theoretical Aspects and Numerical Approximations, SEMA SIMAI Springer Ser., ICIAM 2019 SEMA SIMAI Springer Ser., 8. Springer, Cham, 2021,155-173.
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