  We regard drift-diffusion equations for semiconductor devices in Lebesgue
spaces. To that end we reformulate the (generalized) van Roosbroeck system as
an evolution equation for the potentials to the driving forces of the currents
of electrons and holes. This evolution equation falls into a class of
quasi-linear parabolic systems which allow unique, local in time solution in
certain Lebesgue spaces. In particular, it turns out that the divergence of the
electron and hole current is an integrable function. Hence, Gauss' theorem
applies, and gives the foundation for space discretization of the equations by
means of finite volume schemes. Moreover, the strong differentiability of the
electron and hole density in time is constitutive for the implicit time
discretization scheme. Finite volume discretization of space, and implicit time
discretization are accepted custom in engineering and scientific
computing.--This investigation puts special emphasis on non-smooth spatial
domains, mixed boundary conditions, and heterogeneous material compositions, as
required in electronic device simulation.
