Estimates for the Derivatives of Solutions to Weakly Singular Fredholm Integral Equations

Source abstract

The paper deals with the differential properties of a function $\phi (x)$ defined over a bounded domain in $R^m ,m \geqq 1$, as a solution to a weakly singular Fredholm integral equation of the second kind. Estimates near the boundary of the domain for the derivatives of $\phi (x)$ are given, and an explicit local singular resolution is derived for $\phi (x)$ near a smooth portion of the boundary, assuming that the kernel of the integral equation is of a specific form.