EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 82 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 82
Number of page(s) 34
DOI https://doi.org/10.1051/cocv/2025067
Published online 26 September 2025
  1. E. Cinti, R. Ognibene and B. Ruffini, A quantitative stability inequality for fractional capacities. Math. Eng. 4 (2022) Paper No. 044, 28. [Google Scholar]
  2. S. Shi and J. Xiao, On fractional capacities relative to bounded open Lipschitz sets. Potential Anal. 45 (2016) 261–298. [Google Scholar]
  3. M. Warma, The fractional relative capacity and the fractional Laplacian with Neumann and Robin boundary conditions on open sets. Potential Anal. 42 (2015) 499–547. [CrossRef] [MathSciNet] [Google Scholar]
  4. G. Dal Maso and A. Garroni, New results on the asymptotic behaviour of Dirichlet problems in perforated domains. Math. Models Methods Appl. Sci. 04 (2011) 373–407. [Google Scholar]
  5. G. Dal Maso and F. Murat, Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 24 (1997) 239–290. [Google Scholar]
  6. H. Attouch and C. Picard, Variational inequalities with varying obstacles: the general form of the limit problem. J. Funct. Anal. 50 (1983) 329–386. [Google Scholar]
  7. G. Dal Maso, An introduction to Γ-convergence, in Progress in Nonlinear Differential Equations and their Applications, Vol. 8. Birkhauser Boston, Inc., Boston, MA (1993). [Google Scholar]
  8. G. Dal Maso and U. Mosco, Wiener’s criterion and Γ-convergence. Appl. Math. Optim. 15 (1987) 15–63. [Google Scholar]
  9. A. Ritorto, Optimal partition problems for the fractional Laplacian. Ann. Mat. Pura Appl. 197 (2018) 501–516. [Google Scholar]
  10. A.T. Rauls and G. Wachsmuth, Generalized derivatives for the solution operator of the obstacle problem. Set-Valued Var. Anal. 28 (2020) 259–285. [Google Scholar]
  11. J. Fernández Bonder, A. Ritorto and A.M. Salort, A class of shape optimization problems for some nonlocal operators. Adv. Calc. Var. 11 (2018) 373–386. [Google Scholar]
  12. H. Antil and D. Wachsmuth, Sparse optimization problems in fractional order Sobolev spaces. Inverse Probl. 39 (2023) 044001. (Corrigendum. Inverse Probl. 40 (2024) Paper No. 039501, 3). [Google Scholar]
  13. Q. Fan, Y. Jiao, X. Lu and Z. Sun, Lq-regularization for the inverse Robin problem. J. Inverse Ill-Posed Probl. 24 (2016) 3–12. [Google Scholar]
  14. D. Ghilli and K. Kunisch, On a monotone scheme for nonconvex nonsmooth optimization with applications to fracture mechanics. J. Optim. Theory Appl. 183 (2019) 609–641. [Google Scholar]
  15. B. Wang, W. Wan, Y. Wang, W. Ma, L. Zhang, J. Li, Z. Zhou, H. Zhao and F. Gao, An Lp(0 ≤ p ≤ 1)-norm regularized image reconstruction scheme for breast dot with non-negative-constraint. Biomed. Eng. Online 16 (2017) 32–50. [Google Scholar]
  16. K. Ito and K. Kunisch, Optimal control with Lp(Ω), p ∈ [0,1), control cost. SIAM J. Control Optim. 52 (2014) 1251–1275. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Hintermüller and S. Stengl, Vector-valued convexity of solution operators with application to optimal control problems. WIAS Preprints 2759 (2020) 1-32. https://doi.org/10.20347/WIAS.PREPRINT.2759 [Google Scholar]
  18. A. Fiscella, R. Servadei and E. Valdinoci, Density properties for fractional Sobolev spaces. Ann. Acad. Sci. Fenn. Math. 40 (2015) 235–253. [Google Scholar]
  19. N. Abatangelo and L. Dupaigne, Nonhomogeneous boundary conditions for the spectral fractional Laplacian. Ann. Inst. H. Poincaré C Anal. Non Linéaire 34 (2017) 439–467. [CrossRef] [MathSciNet] [Google Scholar]
  20. H. Antil, J. Pfefferer and M. Warma, A note on semilinear fractional elliptic equation: analysis and discretization. ESAIM Math. Model. Numer. Anal. 51 (2017) 2049–2067. [Google Scholar]
  21. P. Grisvard, Elliptic problems in nonsmooth domains, in Classics in Applied Mathematics, Vol. 69. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2011). [Google Scholar]
  22. J.L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications, Vol. III, Die Grundlehren der mathematischen Wissenschaften, Band 183. Springer-Verlag, New York-Heidelberg (1973), Translated from the French by P. Kenneth. [Google Scholar]
  23. E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136 (2012) 521–573. [Google Scholar]
  24. A. Lentz and D. Wachsmuth, Spatially sparse optimization problems in fractional order Sobolev spaces, Optimization Methods and Software (2025) 1–29. [Google Scholar]
  25. J.F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems. Springer Series in Operations Research. Springer-Verlag, New York (2000). [Google Scholar]
  26. C. Christof and G. Wachsmuth, Semismoothness for solution operators of obstacle-type variational inequalities with applications in optimal control. SIAM J. Control Optim. 61 (2023) 1162–1186. [Google Scholar]
  27. K. Ito and K. Kunisch, A variational approach to sparsity optimization based on Lagrange multiplier theory. Inverse Probl. 30 (2014) 015001, 23. [Google Scholar]
  28. Z. Wei, J. Zhang, Z. Xu, Y. Huang, Y. Liu and X. Fan, Gradient projection with approximate l0 norm minimization for sparse reconstruction in compressed sensing. Sensors 18 (2018) https://www.mdpi.com/1424-8220/18/10/3373. [Google Scholar]
  29. G. Acosta, F.M. Bersetche and J.P. Borthagaray, A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian. Comput. Math. Appl. 74 (2017) 784–816. [Google Scholar]
  30. U. Biccari and V. Hernández-Santamaría, Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects. IMA J. Math. Control Inform. 36 (2019) 1199–1235. [Google Scholar]
  31. H. Antil and J. Pfefferer, A short matlab implementation of fractional Poisson equation with nonzero boundary conditions, Technical report (2017). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.