You can measure the Voltage at the battery when the engine is off with a volt meter. Should be arround 12 volts. When you start the motor, the battery voltage should jump to 13-14 volts and stay there. Note that the actual voltage taken at the alternator and the battery with a volt meter always shows about .3 volts less on the dash voltmeter. If it does not jump up, measure the voltage from the thick red wire on the back of the alternator to ground with the motor running. Should be very close to the battery voltage with the motor on. The 11 volts you desctibe is way too low. It really looks like a bad alternator, but verify it at the battery and alternator with a voltmeter. I've had identical symptoms due to a bad voltage regulator, brush assembly, and rectifier assembly.
You can do a couple of things here:
1. Pull the alternator and take it to Autozone as previously posted or another local parts store equipped with a such tester for free. (I would not feel confident driving there with 11.1 volts.)
2. If it's bad, either purchase a new one for over $100 , or purchase an "alternator repair kit" from Autozone(PN#GMA-03) for $39.99 and rebuilt it yourself. Other parts stores carry "alternator repair kits" as well such as Kragen. It consists of a new rectifier assembly and new brush assembly as well as new bearings and complete steb by step instructions including photos. You can purchase the voltage regulator seperatly elsewere. The tree main componets that go bad in the Delco Remy CS 130 Type alternator found in early C4's are the Rectifier assembly, Voltage regulator, and the Brush assembly. Soldering will be required and maybe an impact wrench to remove the pulley nut if yours is on there pretty good. I rebuilt mine with this kit and my alternator holds voltage at 13.7-14.1 volts at the dash voltmeter. It's been quite a while ago too and saved me the high cost of a new one. So far so good. Good luck.
Edit: Just noticed you live in Sweeden. Not sure what the availability of Vette parts is over there.
Good to hear. Those alternators can be a real PITA. I replaced mine with a junk yard alt. and it pooped 4 months later. Finally paid $150 for a brand new Delco and it's been fine ever since. 
