Comportement des coefficients de Fourier de la solution d’un problème de Dirichlet à domaine polygonal. (Behavior of the Fourier coefficients of the solution of a Dirichlet problem in a polygonal domain). (French) Zbl 0635.35019

Lubuma, Mbaro-Saman

Ann. Soc. Sci. Bruxelles, Sér. I 99(1987), 97-115 (1985).

Near each vertice of a polygonal domain, the solution of the Dirichlet problem (for the Laplacian) is represented by a Fourier series. The formal description of the Fourier coefficients is given for analytic data. It is shown that the ideal spaces for studying the behaviour of the Fourier coefficients are the weighted Sobolev spaces. In these spaces, every Fourier coefficient is split into a regular part and a singular part which is proportional to at most one intrinsic singular function.

MSC:

35J25	Boundary value problems for second-order elliptic equations
35C10	Series solutions to PDEs
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
42B05	Fourier series and coefficients in several variables

Keywords:

polygonal domain; Dirichlet problem; Laplacian; Fourier series; analytic data; weighted Sobolev spaces