Stationary solutions to an energy model for semiconductor devices where the equations are defined on different domains

We discuss a stationary energy model from semiconductor modelling. We accept the more realistic assumption that the continuity equations for electrons and holes have to be considered only in a subdomain Ω 0 of the domain of definition Ω of the energy balance equation and of the Poisson equation. Here Ω 0 corresponds to the region of semiconducting material, Ω \ Ω 0 represents passive layers. Metals serving as contacts are modelled by Dirichlet boundary conditions. We prove a local existence and uniqueness result for the two‐dimensional stationary energy model. For this purpose we derive a W 1, p ‐regularity result for solutions of systems of elliptic equations with different regions of definition and use the Implicit Function Theorem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)