Ein System stationärer partieller Differentialgleichungen des Ladungsträgertransportes in Halbleitern

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.