The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Research Article

The properties of solutions of weakly singular integral equations

G. Vainikko and A. Pedasa1

a1 Department of Applied Mathematics, Tartu State University, 202 400, Tartu, Liivi 2, U.S.S.R.


We examine the differential properties of the solution of the linear integral equation of the second kind, whose kernel depends on the difference of arguments and has an integrable singularity at the point zero. The derivatives of the solution of the equation have singularities at the end points of the domain of integration, and we derive precise estimates for these singularities.

(Received July 22 1980)

(Revised February 05 1981)