La. R.S. 25:761

Where, by reason of topographical conditions, irregularly shaped lots, or because of unusual circumstances applicable solely to the particular applicant, strict enforcement of the provisions of this Part would result in serious undue hardship particularly affecting said applicant, then the commission, in passing upon his application, shall have the power to vary or modify adherence to this Part; provided always that its requirements insure harmony with the general purposes hereof, and will not adversely affect an historic preservation district as a whole or any designated landmark.