@incollection{JEDP_1992____A4_0, author = {Martin Costabel and Monique Dauge}, title = {Singularit\'es d'ar\^etes pour les probl\`emes aux limites elliptiques}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {4}, pages = {1--12}, publisher = {\'Ecole polytechnique}, year = {1992}, mrnumber = {93j:35201}, language = {fr}, url = {https://proceedings.centre-mersenne.org/item/JEDP_1992____A4_0/} }
TY - JOUR AU - Martin Costabel AU - Monique Dauge TI - Singularités d'arêtes pour les problèmes aux limites elliptiques JO - Journées équations aux dérivées partielles PY - 1992 SP - 1 EP - 12 PB - École polytechnique UR - https://proceedings.centre-mersenne.org/item/JEDP_1992____A4_0/ LA - fr ID - JEDP_1992____A4_0 ER -
%0 Journal Article %A Martin Costabel %A Monique Dauge %T Singularités d'arêtes pour les problèmes aux limites elliptiques %J Journées équations aux dérivées partielles %D 1992 %P 1-12 %I École polytechnique %U https://proceedings.centre-mersenne.org/item/JEDP_1992____A4_0/ %G fr %F JEDP_1992____A4_0
Martin Costabel; Monique Dauge. Singularités d'arêtes pour les problèmes aux limites elliptiques. Journées équations aux dérivées partielles (1992), article no. 4, 12 p. https://proceedings.centre-mersenne.org/item/JEDP_1992____A4_0/
[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. | MR | Zbl
[2] B. Andersson, U. Falk, I. BabuKa. 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] 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. | MR | Zbl
[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. | Zbl
[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. | Zbl
[6] M. Costabel, M. Dauge. Construction of corner singularities for Agmon-Douglis-Nirenberg elliptic systems. Preprint Bordeaux, 1992. | Zbl
[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. | Zbl
[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. | MR | Zbl
[9] I. Gohberg, P. Lancaster, L. Rodman. Matrix polynomials. Computer Science and Applied Mathematics. Academic Press, New York 1982. | MR | Zbl
[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. | Zbl
[11] P. Grisvard. Boundary Value Problems in Non-Smooth Domains. Pitman, London 1985.
[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. | MR | Zbl
[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. | MR | Zbl
[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. | Zbl
[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. | MR | Zbl
[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] R. Mazzeo. Elliptic theory of differential edge operators I. Comm. P. D. E. 16 (10) (1991) 1615-1664. | MR | Zbl
[18] R. Melrose. Pseudo-differential operators on manifolds with corners. Manuscript MIT, Boston 1987.
[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. | MR | Zbl
[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. | Zbl
[21] B. W. Schulze. Pseudo-differential operators on manifolds with singularities. Studies in Mathematics and its Applications, Vol. 24. North-Holland, Amsterdam 1991. | MR | Zbl