Singularities of Maxwell interface problems

Martin Costabel; Monique Dauge; Serge Nicaise

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 3, page 627-649
  • ISSN: 0764-583X

How to cite

top

Costabel, Martin, Dauge, Monique, and Nicaise, Serge. "Singularities of Maxwell interface problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.3 (1999): 627-649. <http://eudml.org/doc/193938>.

@article{Costabel1999,
author = {Costabel, Martin, Dauge, Monique, Nicaise, Serge},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {interfaces with edges and corners; harmonic Maxwell equations; transmission problem; edge and corner singularities of the electromagnetic fields},
language = {eng},
number = {3},
pages = {627-649},
publisher = {Dunod},
title = {Singularities of Maxwell interface problems},
url = {http://eudml.org/doc/193938},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Costabel, Martin
AU - Dauge, Monique
AU - Nicaise, Serge
TI - Singularities of Maxwell interface problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 3
SP - 627
EP - 649
LA - eng
KW - interfaces with edges and corners; harmonic Maxwell equations; transmission problem; edge and corner singularities of the electromagnetic fields
UR - http://eudml.org/doc/193938
ER -

References

top
  1. [1] C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional nonsmooth domains. Math.Methods Appl. Sci. 21 (1998) 823-864. Zbl0914.35094MR1626990
  2. [2] F. Assous, P. Ciarlet and E. Sonnendrücker, Résolution des équations de Maxwell dans un domaine avec un coin rentrant. C.R. Acad. Sci. Paris, Ser. I 323 (1996) 203-208. Zbl0855.65131MR1402544
  3. [3] M. Birman and M. Solomyak, L2-theory of the Maxwell operator in arbitrary domains. Russ. Math, Surv. 42 (1987) 75-96. Zbl0653.35075MR933995
  4. [4] M. Birman and M. Solomyak, On the main singularities of the electric component of the electro-magnetic field in regions with screens. St. Petersbg. Math. J. 5 (1993) 125-139. Zbl0804.35127MR1220492
  5. [5] A. Bonnet-BenDhia, C. Hazard and S. Lohrengel, A singular field method for the solution of Maxwell's equations in polyhedral domains. SIAM J. Appl. Math, (to appear). Zbl0933.78007
  6. [6] M. Costabel, A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains. Math. Methods Appl. Sci. 12 (1990) 365-368. Zbl0699.35028MR1048563
  7. [7] M. Costabel, A coercive bilinear form for Maxwell's equations. J. Math. Anal. Appl. 157 (1991) 527-541. Zbl0738.35095MR1112332
  8. [8] M. Costabel and M. Dauge, Singularities of electromagnetic fields in polyhedral domains. Arch. Rational Mech. Anal (to appear). Zbl0968.35113MR1753704
  9. [9] M. Dauge, Elliptic Boundary Value Problems in Corner Domains - Smoothness and Asymptotics of Solutions. Lect. Notes Math. Vol. 1341. Springer-Verlag, Berlin (1988). Zbl0668.35001MR961439
  10. [10] M. Dobrowolski, Numerical approximation of elliptic interface and corner problems. Habilitationsschrift, Bonn (1981). 
  11. [11] P. Fernandes and G. Gilardi, Magnetostatic and electrostatic problems in inhomogeneous anisotropic media with irregular boundary and mixed boundary conditions. Math. Models Methods Appl. Sci. 7 (1997) 957-991. Zbl0910.35123MR1479578
  12. [12] N. Filonov, Système de Maxwell dans des domaines singuliers. Ph.D. thesis, University of Bordeaux 1, France (1996). 
  13. [13] V.A. Kondrat'ev, Boundary-value problems for elliptic equations in domains with conical or angular points. Trans. Moscow Math. Soc, 16 (1967) 227-313. Zbl0194.13405MR226187
  14. [14] T. Kühn, Die Regularität der Lösungen von Interface-Problemen in Gebieten mit singulären Punkten. Ph.D. thesis, University of Rostock (1992). 
  15. [15] D. Leguillon and E. Sanchez-Palencia, Computation of singular solutions in elliptic problems and elasticity. RMA 5. Masson, Paris (1987). Zbl0647.73010MR995254
  16. [16] K. Lemrabet, Régularité de la solution d'un problème de transmission. J. Math. Pures Appl 56 (1977) 1-38. Zbl0366.35036MR509312
  17. [17] M. Moussaoui, Espaces H (div,rot, Ω) dans un polygone plan. C.R. Acad. Sci. Paris, Ser. 7 322 (1996) 225-229. Zbl0852.46034MR1378257
  18. [18] S. Nicaise, Polygonal interface problems. Methoden und Verfahren der Mathematischen Physik, 39. Verlag Peter D. Lang, Frankfurt-am-Main (1993). Zbl0794.35040MR1236228
  19. [19] S. Nicaise and A.M. Sändig, General interface problems I/II. Math. Methods Appl. Sci. 17 (1994) 395-450. Zbl0824.35014MR1274152
  20. [20] J. Saranen, On an inequality of Friedrichs. Math. Scand. 51 (1982) 310-322. Zbl0524.35100MR690534

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.