## Advances in Differential Equations

- Adv. Differential Equations
- Volume 7, Number 7 (2002), 847-876.

### Screening of an applied electric field inside a metallic layer described by the Thomas-Fermi-von Weizsäcker model

X. Blanc and R. Monneau

#### Abstract

We are interested in the effect of a constant electric field on the electronic structure of a crystal. We model it by a density-functional theory, and derive from this microscopic model macroscopic features of the system by letting the ratio $\varepsilon $ between atomic spacing and the size of the crystal go to zero. Although many aspects are disregarded in this approach, we show that the effect of the electric field is negligible inside the crystal and estimate its vanishing rate with respect to the distance from the boundary of the crystal.

#### Article information

**Source**

Adv. Differential Equations, Volume 7, Number 7 (2002), 847-876.

**Dates**

First available in Project Euclid: 27 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1356651708

**Mathematical Reviews number (MathSciNet)**

MR1895168

**Zentralblatt MATH identifier**

1174.82342

**Subjects**

Primary: 82D20: Solids

Secondary: 35A15: Variational methods 35J20: Variational methods for second-order elliptic equations 35J50: Variational methods for elliptic systems 35Q40: PDEs in connection with quantum mechanics 82D35: Metals

#### Citation

Blanc, X.; Monneau, R. Screening of an applied electric field inside a metallic layer described by the Thomas-Fermi-von Weizsäcker model. Adv. Differential Equations 7 (2002), no. 7, 847--876. https://projecteuclid.org/euclid.ade/1356651708