Edge singularities for elliptic boundary value problems

Martin Costabel; Monique Dauge

Journées équations aux dérivées partielles (1992)

  • page 1-12
  • ISSN: 0752-0360

How to cite

top

Costabel, Martin, and Dauge, Monique. "Singularités d'arêtes pour les problèmes aux limites elliptiques." Journées équations aux dérivées partielles (1992): 1-12. <http://eudml.org/doc/93256>.

@article{Costabel1992,
author = {Costabel, Martin, Dauge, Monique},
journal = {Journées équations aux dérivées partielles},
keywords = {edge singularities; edge asymptotics},
language = {fre},
pages = {1-12},
publisher = {Ecole polytechnique},
title = {Singularités d'arêtes pour les problèmes aux limites elliptiques},
url = {http://eudml.org/doc/93256},
year = {1992},
}

TY - JOUR
AU - Costabel, Martin
AU - Dauge, Monique
TI - Singularités d'arêtes pour les problèmes aux limites elliptiques
JO - Journées équations aux dérivées partielles
PY - 1992
PB - Ecole polytechnique
SP - 1
EP - 12
LA - fre
KW - edge singularities; edge asymptotics
UR - http://eudml.org/doc/93256
ER -

References

top
  1. [1] S. AGMON, A. DOUGLIS, L. NIRENBERG. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II. Comm. Pure Appl. Math. 17 (1964) 35-92. Zbl0123.28706MR28 #5252
  2. [2] B. ANDERSSON, U. FALK, I. BABUšKA. Reliable determination of edge and vertex stress intensity factors in three-dimensional elastomechanics. In 17th Congress of the International Council of the Aeronautical Sciences, Stockholm 1990. ICAS-90-4.9.2, pages 1730-1746. AIAA, Washington 1990. 
  3. [3] M. COSTABEL, M. DAUGE. Développement asymptotique le long d'une arête pour des équations elliptiques d'ordre 2 dans ℝ3. C. R. Acad. Sc. Paris, Série I 312 (1991) 227-232. Zbl0722.35021MR92a:35034
  4. [4] M. COSTABEL, M. DAUGE. General edge asymptotics of solutions of second order elliptic boundary value problems I. Publications du Laboratoire d'Analyse Numérique R91016, Université Paris VI 1991. To appear in Proc. Royal Soc. Edinburgh. Zbl0791.35032
  5. [5] M. COSTABEL, M. DAUGE. General edge asymptotics of solutions of second order elliptic boundary value problems II. Publications du Laboratoire d'Analyse Numérique R91017, Université Paris VI 1991. To appear in Proc. Royal Soc. Edinburgh. Zbl0791.35033
  6. [6] M. COSTABEL, M. DAUGE. Construction of corner singularities for Agmon-Douglis-Nirenberg elliptic systems. Preprint Bordeaux, 1992. Zbl0802.35032
  7. [7] M. COSTABEL, M. DAUGE. Edge asymptotics on a skew cylinder. In B.-W. SCHULZE, H. TRIEBEL, editors, Symposium “Analysis in Domains and on Manifolds with Singularities”, Breitenbrunn 1990, Teubner-Texte zur Mathematik, Vol. 131, pages 28-42. B. G. Teubner, Leipzig 1992. Zbl0821.35020
  8. [8] M. DAUGE. Elliptic Boundary Value Problems in Corner Domains — Smoothness and Asymptotics of Solutions. Lecture Notes in Mathematics, Vol. 1341. Springer-Verlag, Berlin 1988. Zbl0668.35001MR91a:35078
  9. [9] I. GOHBERG, P. LANCASTER, L. RODMAN. Matrix polynomials. Computer Science and Applied Mathematics. Academic Press, New York 1982. Zbl0482.15001MR84c:15012
  10. [10] I. GOHBERG, E. SIGAL. An operator generalization of the logarithmic residue theorem and the theorem of Rouché. Math. USSR Sbornik 13 (4) (1971) 603-625. Zbl0254.47046
  11. [11] P. GRISVARD. Boundary Value Problems in Non-Smooth Domains. Pitman, London 1985. Zbl0695.35060
  12. [12] 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. Zbl0194.13405MR37 #1777
  13. [13] V. A. KONDRAT'EV. Singularities of a solution of Dirichlet's problem for a second order elliptic equation in a neighborhood of an edge. Differential Equations 13 (1970) 1411-1415. Zbl0394.35027MR58 #6668
  14. [14] V. G. MAZ'YA, B. A. PLAMENEVSKII. Lp estimates of solutions of elliptic boundary value problems in a domain with edges. Trans. Moscow Math. Soc. 1 (1980) 49-97. Zbl0453.35025
  15. [15] V. G. MAZ'YA, J. ROSSMANN. Über die Asymptotik der Lösungen elliptischer Randwertaufgaben in der Umgebung von Kanten. Math. Nachr. 138 (1988) 27-53. Zbl0672.35020MR90a:35079
  16. [16] V. G. MAZ'YA, J. ROSSMANN. On the asymptotics of solutions to the Dirichlet problem for second order elliptic equations in domains with critical angles on the edges. Preprint LiTH-MAT-R-91-37, Linköping University 1991. 
  17. [17] R. MAZZEO. Elliptic theory of differential edge operators I. Comm. P. D. E. 16 (10) (1991) 1615-1664. Zbl0745.58045MR93d:58152
  18. [18] R. MELROSE. Pseudo-differential operators on manifolds with corners. Manuscript MIT, Boston 1987. 
  19. [19] V. A. NIKISHKIN. Singularities of the solution of the Dirichlet problem for a second order equation in a neighborhood of an edge. Moscow Univ. Math. Bull. 34(2) (1979) 53-64. Zbl0433.35027MR80h:35046
  20. [20] B. SCHMUTZLER. About the structure of branching asymptotics for elliptic boundary value problems in domains with edges. In B.-W. SCHULZE, H. TRIEBEL, editors, Symposium “Analysis in Domains and on Manifolds with Singularities”, Breitenbrunn 1990, Teubner-Texte zur Mathematik, Vol. 131, pages 202-208. B. G. Teubner, Leipzig 1992. Zbl0823.35049
  21. [21] B. W. SCHULZE. Pseudo-differential operators on manifolds with singularities. Studies in Mathematics and its Applications, Vol. 24. North-Holland, Amsterdam 1991. Zbl0747.58003MR93b:47109

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.