(a) In accordance with a comprehensive plan adopted under AS 29.40.030 and in order to implement the plan, the assembly by ordinance shall adopt or amend provisions governing the use and occupancy of land that may include, but are not limited to,

1. (1) zoning regulations restricting the use of land and improvements by geographic districts;
2. (2) land use permit requirements designed to encourage or discourage specified uses and construction of specified structures, or to minimize unfavorable effects of uses and the construction of structures;
3. (3) measures to further the goals and objectives of the comprehensive plan.

(b) A variance from a land use regulation adopted under this section may not be granted if

1. (1) special conditions that require the variance are caused by the person seeking the variance;
2. (2) the variance will permit a land use in a district in which that use is prohibited; or
3. (3) the variance is sought solely to relieve pecuniary hardship or inconvenience.