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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)].

35C20 Asymptotic expansions of solutions to PDEs
35J40 Boundary value problems for higher-order elliptic equations
Full Text: DOI EuDML
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