Abstract
In this chapter we present existence, regularity, uniqueness and continuous-dependence-on-data results for the basic semiconductor device equations in the stationary case. The analysis will heavily rely on the modern abstract theory of elliptic differential equations and on functional analysis. The results on elliptic boundary value problems, which we shall use in the sequel, can be found in the references [3.7], [3.10], [3.14], [3.20], [3.32], the concepts from functional analysis in [3.5], [3.6], [3.10], [3.13], [3.21], [3.32] and the theory of Sobolev spaces in [3.1]. A list of notations is compiled in the Appendix.KeywordsWeak SolutionEquilibrium SolutionSemiconductor DeviceImplicit Function TheoremIteration SchemeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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