What happens if I use a DC adapter with a15v output with a PC monitor with a 14v rating?
The power adapter probably feeds into a number of voltage regulators or DC to DC voltage converters so the circuits will get the proper voltages ahead of the adapter.  Equipment is designed so that it can handle a certain range of voltages to allow for voltage drift caused by aging components and/or other problems caused by open capacitors etc. I have never needed to change an adapter for a monitor but have replaced adapters that were not exactly the same voltage as the original for laptops and other equipment and have had no problems.  If this were my equpment, I would try the adapter provided it was the same polarity.  Reverse polarity will definitely damage the equipment but one volt higher probably won't make any difference.