Centre de Mathématiques Appliquées, Ecole Polytechnique
About some operators over a unit disc related to the Laplace equation
We introduce variational formulations for the weakly-singular and hyper-singular operators, as well as for their corresponding inverses, associated to the Laplace operator in the domain of R³ exterior to a flat open disk in R³. Using adequate basis functions on the disk, we obtain an exact expression for the associated kernels of these four operators. This work is an extension to R³ of the article by Jerez-Hanckes and Nédélec (2012, Explicit variational forms for the inverses of integral logarithmic operators over an interval)
