On the regularity of solutions to volterra functional integro-differential equations with weakly singular kernels

Abstract

We study the regularity properties of solutions for various classes of Volterra functional integrodifferential equations with nonvanishing delays and weakly singular kernels. In particular, we characterize equations in which "supersmoothing," smoothing, or no smoothing occurs at the primary discontinuity points induced by the nonvanishing delay. These results will play a crucial role in the design and analysis of methods for the numerical solution of such functional equations with nonsmooth solutions. © 2006 Rocky Mountain Mathematics Consortium.