Eruv and Mezuzah — Eruvin 74b
תלמוד בבלי מסכת עירובין דף עד/ב
ואיבות בר איהי סבר מקום פיתא גרים ושמואל לטעמיה דאמר מקום לינה גרים
The Gemara cites the dispute as to the determination of a person's primary "place" for the purposes of participation in an eruv: Is the person's place to eat primary, or his place to sleep primary.
Teshuvos BeTzel HaChochmah (3:84) asserts that this definition is applicable to the laws of mezuzah as well: Only rooms that can be classified as a place for eating or a place for sleeping (or a room that serves as a passageway into one of these rooms) need to have a mezuzah. Hence, rules the BeTzel HaChochmah, the doors of elevators are exempt from mezuzos: the elevators are not places of eating or sleeping (nor can they be liable to have a mezuzah as a room leading into one of these rooms, as the impermanence of the elevator cabin's location precludes its doors from being considered a passageway).
However, Teshuvos Avnei Nezer (in several responsa — see, for example, Yoreh Deah §382) suggests that the parameters of mezuzah are not comparable to the parameters of eruvin. Hence, a room used by a woman to apply cosmetics and to beautify her self is liable to have a mezuzah, even though she never sleeps nor eats there. It must be, asserts the Avnei Nezer, that it is only because eruvin are a Rabbinic enactment that a more lenient standard is applied here and that a place need not be taken into account unless it serves for eating or sleeping.