Solution of a 2-D weakly singular integral equation with constraint (Q1894921)

The author studies a two-dimensional weakly singular integral equation of the first kind where the unknown function is subject to a constraint. This equation extends the classical integral equations due to Hertz (1881) describing contact problems for elastic balls and general elastic solids. Using integral mean value theorems and the Radon transform, the given integral equation is reduced to a standard one-dimensional Abel integral equation and thereby the author obtains the required solution in a closed form. The latter agrees with the specialized Hertz's solutions which were conjectured by Hertz. The method can also be extended to the three-dimensional case.