Strong Solutions of Quasilinear Integro-Differential Equations with Singular Kernels in Several Space Dimensions

Abstract

For quasilinear integro-differential equations of the form ut − a ∗ A(u) = f , where a is a scalar singular integral kernel that behaves like t−α, 1 ≤ α < 1 and A is a second order quasilinear elliptic operator in divergence form, solutions are found for which A(u) is integrable over space and time.