(a) The zoning board of appeals shall have the following powers and duties: (1) To hear and decide appeals where it is alleged that there is an error in any order, requirement or decision made by the official charged with the enforcement of this chapter or any bylaw, ordinance or regulation adopted under the provisions of this chapter; (2) to hear and decide all matters including special exceptions and special exemptions under section 8-2g upon which it is required to pass by the specific terms of the zoning bylaw, ordinance or regulation; and (3) to determine and vary the application of the zoning bylaws, ordinances or regulations in harmony with their general purpose and intent and with due consideration for conserving the public health, safety, convenience, welfare and property values solely with respect to a parcel of land where, owing to conditions especially affecting such parcel but not affecting generally the district in which it is situated, a literal enforcement of such bylaws, ordinances or regulations would result in exceptional difficulty or unusual hardship so that substantial justice will be done and the public safety and welfare secured, provided that the zoning regulations may specify the extent to which uses shall not be permitted by variance in districts in which such uses are not otherwise allowed. No such board shall be required to hear any application for the same variance or substantially the same variance for a period of six months after a decision by the board or by a court on an earlier such application.

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(b) Any variance granted by a zoning board of appeals shall run with the land and shall not be personal in nature to the person who applied for and received the variance. A variance shall not be extinguished solely because of the transfer of title to the property or the invalidity of any condition attached to the variance that would affect the transfer of the property from the person who initially applied for and received the variance.