EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 58 / No 2 (March-April 2024) ESAIM: M2AN, 58 2 (2024) 545-569 References
Open Access
Issue
ESAIM: M2AN
Volume 58, Number 2, March-April 2024
Page(s) 545 - 569
DOI https://doi.org/10.1051/m2an/2024003
Published online 09 April 2024
  1. G.S. Alberti and Y. Capdeboscq, Elliptic regularity theory applied to time harmonic anisotropic Maxwell’s equations with less than Lipschitz complex coefficients. SIAM J. Math. Anal. 46 (2014) 998–1016. [CrossRef] [MathSciNet] [Google Scholar]
  2. H. Ammari, J. Garnier, W. Jing, H. Kang, M. Lim, K. Sølna and H. Wang, Mathematical and Statistical Methods for Multistatic Imaging. Springer, New York (2013). [CrossRef] [Google Scholar]
  3. E. Blåsten, Nonradiating sources and transmission eigenfunctions vanish at corners and edges. SIAM J. Math. Anal. 50 (2018) 6255–6270. [CrossRef] [MathSciNet] [Google Scholar]
  4. E. Blåsten and H. Liu, On vanishing near corners of transmission eigenfunctions. J. Funct. Anal. 273 (2017) 3616–3632. [CrossRef] [MathSciNet] [Google Scholar]
  5. E. Blåsten and H. Liu, On corners scattering stably and stable shape determination by a single far-field pattern. Indiana Univ. Math. J. 70 (2021) 907–947. [CrossRef] [MathSciNet] [Google Scholar]
  6. E. Blåsten and H. Liu, Scattering by curvatures, radiationless sources, transmission eigenfunctions, and inverse scattering problems. SIAM J. Math. Anal. 53 (2021) 3801–3837. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. Blåsten, X. Li, H. Liu and Y. Wang, On vanishing and localizing of transmission eigenfunctions near singular points: a numerical study. Inverse Probl. 33 (2017) 105001. [CrossRef] [Google Scholar]
  8. E. Blåsten, H. Liu and J. Xiao, On an electromagnetic problem in a corner and its applications. Anal. PDE 14 (2021) 2207–2224. [CrossRef] [MathSciNet] [Google Scholar]
  9. A. Buffa, M. Costabel and D. Sheen, On traces for H(curl, Ω) in Lipschitz domain. J. Math. Anal. Appl. 276 (2002) 845–876. [CrossRef] [MathSciNet] [Google Scholar]
  10. F. Cakoni and D. Colton, Qualitative Methods in Inverse Scattering Theory. Springer, Berlin (2006). [Google Scholar]
  11. F. Cakoni, D. Colton and P. Monk, The electromagnetic inverse-scattering problem for partly coated Lipschitz domains. Proc. R. Soc. Edinb. Sect. A Math. 134 (2004) 661–682. [CrossRef] [Google Scholar]
  12. F. Cakoni, D. Colton and P. Monk, The Linear Sampling Method in Inverse Electromagnetic Scattering. SIAM, Philadelphia (2011). [CrossRef] [Google Scholar]
  13. F. Cakoni, D. Colton and H. Haddar, Inverse Scattering Theory and Transmission Eigenvalues. SIAM, Philadelphia (2016). [CrossRef] [Google Scholar]
  14. X. Cao, H. Diao, H. Liu and J. Zou, On nodal and generalized singular structures of Laplacian eigenfunctions and applications to inverse scattering problems. J. Math. Pures Appl. 143 (2020) 116–161. [CrossRef] [MathSciNet] [Google Scholar]
  15. X. Cao, H. Diao, H. Liu and J. Zou, On novel geometric structures of Laplacian eigenfunctions in R3 and applications to inverse problems. SIAM J. Math. Anal. 53 (2021) 1263–1294. [CrossRef] [MathSciNet] [Google Scholar]
  16. Y.-T. Chow, Y. Deng, Y. He, H. Liu and X. Wang, Surface-localized transmission eigenstates, super-resolution imaging and pseudo surface plasmon modes. SIAM J. Imaging Sci. 14 (2021) 946–975. [CrossRef] [MathSciNet] [Google Scholar]
  17. Y.-T. Chow, Y. Deng, H. Liu and M. Sunkula, Surface concentration of transmission eigenfunctions. Arch. Ration. Mech. Anal. 247 (2023) 48. [CrossRef] [Google Scholar]
  18. S. Cogar and P. Monk, Modified electromagnetic transmission eigenvalues in inverse scattering theory. SIAM J. Math. Anal. 52 (2020) 6412–6441. [CrossRef] [MathSciNet] [Google Scholar]
  19. D. Colton and R. Kress, On the denseness of Herglotz wave functions and electromagnetic Herglotz pairs in Sobolev spaces. Math. Meth. Appl. Sci. 24 (2001) 1289–1303. [CrossRef] [Google Scholar]
  20. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 4th edition. Springer, New York (2019). [CrossRef] [Google Scholar]
  21. Y. Deng, C. Duan and H. Liu, On vanishing near corners of conductive transmission eigenfunctions. Res. Math. Sci. 9 (2022) 2. [CrossRef] [MathSciNet] [Google Scholar]
  22. Y. Deng, Y. Jiang, H. Liu and K. Zhang, On new surface-localized transmission eigenmodes. Inverse Probl. Imaging 16 (2022) 595–611. [CrossRef] [MathSciNet] [Google Scholar]
  23. Y. Deng, H. Liu, X. Wang and W. Wu, On geometric properties of electromagnetic transmission eigenfunctions and artificial mirage. SIAM J. Appl. Math. 82 (2022) 1–24. [CrossRef] [MathSciNet] [Google Scholar]
  24. H. Diao and H. Liu, Spectral Geometry and Inverse Scattering Theory. Springer, Cham (2023). [CrossRef] [Google Scholar]
  25. H. Diao, H. Liu, X. Wang and K. Yang, On vanishing and localizing around corners of electromagnetic transmission resonances. Partial Differ. Equ. Appl. 2 (2021) 1–20. [CrossRef] [Google Scholar]
  26. H. Diao, X. Cao and H. Liu, On the geometric structures of transmission eigenfunctions with a conductive boundary condition and applications. Commun. Partial Differ. Equ. 46 (2021) 630–679. [CrossRef] [Google Scholar]
  27. H. Diao, H. Li, H. Liu and J. Tang, Spectral properties of an acoustic-elastic transmission eigenvalue problem with applications. J. Differ. Equ. 371 (2023) 629–659. [CrossRef] [Google Scholar]
  28. Y. Gao, H. Liu, X. Wang and K. Zhang, On an artificial neural network for inverse scattering problems. J. Comput. Phys. 448 (2022) 110771. [CrossRef] [Google Scholar]
  29. Y. He, H. Liu and X. Wang, A novel quantitative inverse scattering scheme using interior resonant modes. Inverse Probl. 39 (2023) 085002. [CrossRef] [Google Scholar]
  30. Y. Jiang, H. Liu, J. Zhang and K. Zhang, Spectral patterns of elastic transmission eigenfunctions: boundary localization, surface resonance, and stress concentration. SIAM J. Appl. Math. 83 (2023) 2469–2498. [CrossRef] [MathSciNet] [Google Scholar]
  31. Y. Jiang, H. Liu, J. Zhang and K. Zhang, Boundary localization of transmission eigenfunctions in spherically stratified media. Asymptot. Anal. 132 (2023) 285–303. [MathSciNet] [Google Scholar]
  32. A. Kirsch and P. Monk, A finite element/spectral method for approximating the time-harmonic Maxwell system in R3. SIAM J. Appl. Math. 55 (1995) 1324–1344. [CrossRef] [MathSciNet] [Google Scholar]
  33. A. Kirsch and F. Hettlich, The Mathematical Theory of Time-Harmonic Maxwell’s Equations. In Vol. 190 of Applied Mathematical Sciences. Springer (2015). [CrossRef] [Google Scholar]
  34. J. Li and H. Liu, Numerical methods for inverse scattering problems. Springer, Singapore (2023). [Google Scholar]
  35. J. Li, H. Liu and Q. Wang, Enhanced multilevel linear sampling methods for inverse scattering problems. J. Comput. Phys. 257 (2014) 554–571. [CrossRef] [MathSciNet] [Google Scholar]
  36. H. Li, S. Li, H. Liu and X. Wang, Analysis of electromagnetic scattering from plasmonic inclusions beyond the quasi-static approximation and applications. ESAIM: Math. Model. Numer. Anal. 53 (2019) 1351–1371. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  37. H. Liu, On local and global structures of transmission eigenfunctions and beyond. J. Inverse III-Posed Probl. 30 (2022) 287–305. [CrossRef] [MathSciNet] [Google Scholar]
  38. H. Liu, Y. Wang, and S. Zhong, Nearly non-scattering electromagnetic wave set and its application. Z. Angew. Math. Phys. 68 (2017) 35. [CrossRef] [Google Scholar]
  39. H. Liu, X. Liu, X. Wang and Y. Wang, On a novel inverse scattering scheme using resonant modes with enhanced imaging resolution. Inverse Probl. 35 (2019) 125012. [CrossRef] [Google Scholar]
  40. P. Monk, Finite Element Methods for Maxwell’s Equations. Oxford University Press, New York (2003). [Google Scholar]
  41. P. Monk and J. Sun, Finite element methods for Maxwell’s transmission eigenvalues. SIAM J. Sci. Comput. 34 (2012) B247–B264. [CrossRef] [Google Scholar]
  42. L. Wang, Q. Zhang, J. Sun and Z. Zhang, A priori and a posteriori error estimates for the quad-curl eigenvalue problem. ESAIM: Math. Model. Numer. Anal. 56 (2022) 1027–1051.s [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  43. W. Yin, W. Yang and H. Liu, A neural network scheme for recovering scattering obstacles with limited phaseless far-field data. J. Comput. Phys. 417 (2020) 18. [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.

Recommended for you