Zeitschrift für Analysis und ihre Anwendungen
Full-Text PDF (240 KB) | Metadata | Table of Contents | ZAA summary
Published online: 2006-12-31
Integral Equations with Diagonal and Boundary Singularities of the KernelArvet Pedas and Gennadi Vainikko (1) Tartu University, Estonia
(2) Tartu University, Estonia
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.
Keywords: Fredholm integral equation, Volterra integral equation, weakly singular integral equation, boundary singularities, smoothness of the solution, compact operators
Pedas Arvet, Vainikko Gennadi: Integral Equations with Diagonal and Boundary Singularities of the Kernel. Z. Anal. Anwend. 25 (2006), 487-516. doi: 10.4171/ZAA/1304