Solutions for the amorphous silicon system and related problems

We present existence of solutions and other results for the partial differential equation system with memory which models amorphous silicon devices and related problems in ${Bbb R}^3$. Our approach employs only classical estimates and Degree Theory; it shows the existence of $C^{alpha,alpha/2}$ solutions for some $alpha>0$. In view of the mixed boundary conditions, this is the maximum regularity that can be expected.