Sharp estimates of solution of an elliptic problem on a family of open
non-convex planar sectors
Abstract
Based on partial Fourier series analysis, we adapt on a model case a new
approach to classical results obtained in the literature describing the
singularities of a family a solutions of a second order elliptic
problems on open non-convex planar sectors. The method allows the
exhibition of singular and regular frequencies, explicit decomposition
and description of coefficients of singularities of the solution. As a
main result, explicit and sharp estimates with respect to the opening
angle parameter are obtained via this method. They are not uniform near
π where corners have opening angle generating a jump of
singularity in Sobolev exponent, contrarily to the results obtained in
A. Tami (2016),(2019),(2021) for harmonic and/or biharmonic problems on
a family of convex planar sectors.