# Integral Equations with Diagonal and Boundary Singularities of the Kernel

### Arvet Pedas

Tartu University, Estonia### Gennadi Vainikko

Tartu University, Estonia

## Abstract

We study the smoothness and the singularities of the solution to Fredholm and Volterra integral equations of the second kind on a bounded interval. The kernel of the integral operator may have diagonal and boundary singularities, information about them is given through certain estimates. The weighted spaces of smooth functions with boundary singularities containing the solution of the integral equation are described. Examples show that the results cannot be improved.

## Cite this article

Arvet Pedas, Gennadi Vainikko, Integral Equations with Diagonal and Boundary Singularities of the Kernel. Z. Anal. Anwend. 25 (2006), no. 4, pp. 487–516

DOI 10.4171/ZAA/1304