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Zeitschrift für Analysis und ihre Anwendungen

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Volume 25, Issue 4, 2006, pp. 487–516
DOI: 10.4171/ZAA/1304

Published online: 2006-12-31

Integral Equations with Diagonal and Boundary Singularities of the Kernel

Arvet Pedas[1] and Gennadi Vainikko[2]

(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