Multiscale modeling of fluctuations in stochastic elliptic PDE models of nanosensors (Q743929)

The homogenization of boundary layers in stochastic elliptic partial differential equations is studied. The main result is a limiting problem for the covariance of the solution of the stochastic equation. The existence and uniqueness results, a rate for the covariance and further properties of the limiting problem are derived. A discretization for the limiting problem is presented and numerical approximation of the solution are discussed. Applications of this work include the simulation of electrostatics in nanotechnological devices such as field-effect sensors.