Coefficients of the singularities on domains with conical points

• Autorzy: Monique Dauge , Serge Nicaise
• Języki publikacji: EN

Abstrakty

EN

As a model for elliptic boundary value problems, we consider the Dirichlet problem for an elliptic operator. Solutions have singular expansions near the conical points of the domain. We give formulas for the coefficients in these expansions.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1992
• Tom: 27
• Numer: 1
• Strony: 91-99

Daty

wydano

1992

Twórcy

autor

Monique Dauge

• Département de Mathématiques, Université de Nantes, U.R.A. C.N.R.S. 758, 2, rue de la Houssinière, F-44072 Nantes Cedex 03, France

autor

Serge Nicaise

• U.F.R. de Mathématiques Pures et Appliquées, Université des Sciences et Techniques, de Lille Flandres Artois, U.R.A. C.N.R.S. 751, F-59655 Villeneuve D'Ascq Cedex, France

Bibliografia

• [1] M. Dauge, Elliptic Boundary Value Problems in Corner Domains--% Smoothness and Asymptotics of Solutions, Lecture Notes in Math. 1341, Springer, Berlin 1988.
• [2] M. Dauge, S. Nicaise, M. Bourlard et M. S. Lubuma, Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques I: résultats généraux pour le problème de Dirichlet, Math. Modelling Numer. Anal. 24 (1) (1990), 27-52.
• [3] M. Dauge, S. Nicaise, M. Bourlard et M. S. Lubuma, Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques II: quelques opérateurs particuliers, ibid. 24 (3) (1990), 343-367.
• [4] 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.
• [5] V. A. Kozlov and V. G. Maz'ya, Estimates of $L_p$-means and asymptotics of solutions of elliptic boundary value problems in a cone, II. Operators with variable coefficients, Math. Nachr. 137 (1988), 113-139 (in Russian).
• [6] V. G. Maz'ya and B. A. Plamenevskiĭ, Coefficients in the asymptotics of the solutions of an elliptic boundary value problem in a cone, Amer. Math. Soc. Transl. (2) 123 (1984), 57-88.
• [7] V. G. Maz'ya and B. A. Plamenevskiĭ, On the asymptotics of the fundamental solution of elliptic boundary value problem in a region with conical points, Selecta Math. Sov. 4 (4) (1985), 363-397.