12V for a 10.5V netbook?
The topic is more complicated than you think. Yes, 12V can be reduced to 10.5V with a DC/DC converter (assuming a high current), or, you can just get a car inverter that takes an input of 12V (just like in the car), converts it to 110/220 and then you use your own adapter. This will work (except for some more loss).

The bigger issue is that the 12V is not likely constant. Depending on the sun and other factors it will vary and at some point the inverter won't be able to provide power and everything will come crashing down. So the issue needs to be addressed with some backup battery or some other system (switch over to AC for example).