JournalszaaVol. 25 , No. 4DOI 10.4171/zaa/1304

Integral Equations with Diagonal and Boundary Singularities of the Kernel

  • Arvet Pedas

    Tartu University, Estonia
  • Gennadi Vainikko

    Tartu University, Estonia
Integral Equations with Diagonal and Boundary Singularities of the Kernel cover

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.