An application of the implicit function theorem to an energy model of the semiconductor theory

In this paper we deal with a mathematical model for the description of heat conduction and carrier transport in semiconductor heterostructures. We sol ve a coupled system of nonlinear elliptic differential equations consisting of the heat equation with Joule heating as a source, the Poisson equation for the electric field and drift-diffusion equations with temperature depen dent coefficients describing the charge and current conservation; subject t o general thermal and electrical boundary conditions. We prove the existenc e and uniqueness of Holder continuous weak solutions near thermodynamic equ ilibria points using the Implicit Function Theorem. To show the continuous differentiability of maps corresponding to the weak formulation of the prob lem we use regularity results from the theory of nonsmooth linear elliptic boundary value problems in Sobolev-Campanato spaces.