  This paper concerns a time-independent thermoelectric model with two
different boundary conditions. The model is a nonlinear coupled system of the
Maxwell equations and an elliptic equation. By analyzing carefully the
nonlinear structure of the equations, and with the help of the De Giorgi-Nash
estimate for elliptic equations, we obtain existence of weak solutions on
Lipschitz domains for general boundary data. Using Campanato's method, we
establish regularity results of the weak solutions.
