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Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques. I: Résultats généraux pour le problème de Dirichlet. (Singularity coefficients for boundary value problems in domains with conical points. I: General results for the Dirichlet problem). (French) Zbl 0691.35023
Summary: It is well known that a solution of a boundary value problem on a domain with conical points may be split into a regular and a singular part. The singular part is a linear combination of a finite set of functions which only depend on the domain and on the operator. We give formulae for those coefficients in relation to the right-hand side of the equation and to the solution. In that first part, we study the Dirichlet problem, for an operator with smooth coefficients on an n-dimensional domain. Our formulae hold in a wider functional framework than the one which was given by V. G. Maz’ya and B. A. Plamenevskij [Transl., II. Ser., Am. Math. Soc. 123, 57-88 (1984; Zbl 0554.35036)].

MSC:
35C20 Asymptotic expansions of solutions to PDEs
35J40 Boundary value problems for higher-order elliptic equations
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References:
[1] M. DAUGE: Elliptic boundary value problems in corner domains; smoothness and asymptotics of solutions. Lect. Notes in Math. 1341, Springer-Verlag (1988). Zbl0668.35001 MR961439 · Zbl 0668.35001
[2] M. DAUGE, M. S. LUBUMA et S. NICAISE: Coefficients des singularités pour le problème de Dirkhlet sur un polygone. C.R. Acad. Sc. Paris 304, Série I, 16, 483-486 (1987). Zbl0619.35033 MR894574 · Zbl 0619.35033
[3] P. GRISVARD: Elliptic problems in non smooth domains. Monographes and Studies in Math. 24, Pitman (1985). Zbl0695.35060 · Zbl 0695.35060
[4] V. A. KONDRAT’EV: Boundary-value problems for elliptic equations in domains with conical or angular points. Trans. Moscow Math. Soc. 16, 227-313 (1967). Zbl0194.13405 MR226187 · Zbl 0194.13405
[5] J. L. LIONS et E. MAGENES: Problèmes aux limites non homogènes. Vol. I, Dunod, 1967.
[6] D. LEGUILLON et E. SANCHEZ-PALENCIA: Computation of singular solutions in elliptic problems and elasticity. RMA 5, Masson (1987). Zbl0647.73010 MR995254 · Zbl 0647.73010
[7] V. G. MAZ’YA et B. A. PLAMENEVSKII: Estimates in Lp and in Hölderclasses and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary. A.M.S. Transl. (2), 123, 1-56 (1984). Zbl0554.35035 · Zbl 0554.35035
[8] V. G. MAZ’YA et B. A. PLAMENEVSKII: Coefficients in the asymptotics of the solutions of an elliptic boundary value problem in a cone. A.M.S. Transl.(2), 123, 57-88 (1984). Zbl0554.35036 · Zbl 0554.35036
[9] V. G. MAZ’YA et B. A. PLAMENEVSKII: On the coefficients in the asymptotics of the solutions of an elliptic boundary value problem in domains with conical points. J. of Soviet. Math. 9, 5, 750-764 (1978). Zbl0396.35038 · Zbl 0396.35038
[10] V. G. MAZ’YA et B. A. PLAMENEVSKII: Lp estimates of solutions of elliptic boundary value problems in a domain with edges. Trans. Moscow Math. Soc. 1, 49-97 (1980). Zbl0453.35025 · Zbl 0453.35025
[11] M. A. MOUSSAOUI: Sur l’approximation des solutions du problème de Dirichle dans un ouvert avec coins. Singularities and constructive methods for their treatment P. Grisvard, W. Wendland, J. R. Whiteman éditeurs. Lecture Notes in Mathematics n^\circ 1121,Springer Verlag, 1985,199-206. Zbl0575.65102 MR806394 · Zbl 0575.65102
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