Abstract
Different boundary value problems for the system of stationary partial differential equations for the carrier transport in semiconductors are considered in corresponding subspaces of the product $W_r^1(G) \\times W_p^1(G) \\times W_p^1(G)$ with Sobolev-spaces $W_q^1(G), q = r$ and $q = p$. The domain $G \\subset \\mathbb R^n (n = 1,2,3)$ is supposed to be bounded and $p$ and $r$ are in general different. The paper contains the proof of the existence of solutions in the whole scale $2n/(n + 1) < p < + \\infty$ with corresponding restrictions for $r > 1$, estimations from above for the diameter of the solution set and some uniqueness results.
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