On the coefficients of singularity of a bi-harmonic problem on a truncated non-convex sector near the angle π by Fourier analysis

Based on Fourier series, we adapt an approach discussed in a recent work on the Laplace operator to classical results obtained in the literature, describing the singularities of solutions to a fourth-order elliptic problem on a polygonal domain of the plane that may appear near a concave corner. We demonstrate how the Fourier series method provides explicit decomposition and precise description of the coefficients of singularities of the solution. As a main result, explicit and sharp estimates with respect to the opening angle parameter can be obtained via this method. We recall that such estimates can be useful for the asymptotic analysis of solutions near corners where the opening angle generates a jump in singularity in Sobolev's exponent.