Coefficients des singularités pour le problème de Dirichlet sur un polygone. (Coefficients of singularities for the Dirichlet problem in a polygon). (French) Zbl 0619.35033

The authors state two types of formulas for the coefficients of singular functions appearing in the asymptotics of the solution of the Dirichlet problem on a polygonal domain \(\Omega\), when the data are in classical or weighted Sobolev spaces. One of these types of formulas defines a continuous linear form only depending on the data; some of theses formulas are localized on the vertices of \(\Omega\), the others are global on \(\Omega\). The other type of formulas is an expression related to the solution.


35J25 Boundary value problems for second-order elliptic equations
35A20 Analyticity in context of PDEs