Smoothness in the Dini Space of a Single Layer Potential for a Parabolic System in the Plane

Resumo

We prove estimates in the Dini space for the second order spatial derivative of a vector parabolic single layer potential. We obtain estimates for higher order derivatives of solutions to initial-boundary-value problems for one-dimensional parabolic systems with Dini-continuous coefficients in a curvilinear domain with nonsmooth lateral boundary.