where h ∈ L1(0,T ;X) and f : [0,T ]×X →X. This is obtained if one takes F(u)(t)= h(t)−∫ t 0 a(t−s)f (s,u(s))ds in (1.1). Such problems are important from the viewpoint of applications since they cover nonlocal generalizations of integrodifferential equations arising in the mathematical modeling of heat conduction in materials with memory. Byszewski [6, 7] initiated the work concerning abstract ...

Abstract We study robust regularity estimates for local minimizers of nonlocal functionals with non-standard growth ( p , q )-type and weak solutions to a related class equations. The main results this paper are boundedness Hölder continuity solutions. Our approach is based on the corresponding De Giorgi classes.