WIAS Preprint No. 1173, (2006)

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


  • Glitzky, Annegret
    ORCID: 0000-0003-1995-5491
  • Hünlich, Rolf

2010 Mathematics Subject Classification

  • 35J55 35A07 35R05 80A20


  • Energy models, mass, charge and energy transport in heterostructures, strongly coupled elliptic systems, mixed boundary conditions, Implicit Function Theorem, existence; uniqueness, regularity




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 $Omega_0$ of the domain of definition $Omega$ of the energy balance equation and of the Poisson equation. Here $Omega_0$ corresponds to the region of semiconducting material, $OmegasetminusOmega_0$ 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.

Appeared in

  • Math. Nachr., 281 (2008) pp. 1676--1693.

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