Like Spain to Italy something because that's no border between
Some airlines like Ryanair will not allow non-EU/EEA passengers to travel with just a mobile boarding pass, because they want you to do a "document check" and have something to put a stamp onto, so they need something in paper form (which you should print at home, because they will charge you gazillions for printing anything for you).
However, generally, yes, mobile boarding passes are possible and quite frequent, though the exact details will vary from airline to airline, and possibly from one flight to another depending on the departure and destination airports. They are actually quite common for non-Schengen flights as well, this is quite unrelated.
Note that even though there should be no systematic checks of passports and visas at internal Schengen borders or before or after internal Schengen flights, you may still be faced with temporarily re-introduced checks (current list) or spot checks.