Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients

We investigate linear and quasilinear evolutionary partial integro-differential equations of second order which include time fractional evolution equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration technique we establish results asserting the global boundedness of appropriately defined weak solutions of these problems. We also show that a maximum principle holds for such equations. (C) 2008 Elsevier Inc. All rights reserved.