Energy models where the equations are defined on different domains

We investigate a stationary energy model for semiconductor devices and respect the more realistic assumption that the continuity equations for electrons and holes have to be investigated only in a subdomain Ω₀ of the domain of definition Ω of the energy balance equation and of the Poisson equation. This nonlinear system of model equations is strongly coupled and has to be considered in heterostructures and with mixed boundary conditions. We obtain 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. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)