Both Christmas and New Year is in Norway by most people celebrated at home. It would be very unusual for a Norwegian family to go out on Christmas Eve. You must expect most restaurants to be closed on December 24th, 25th and 31st and on January 1st. Even between Christmas and New Year, many restaurants are closed, many shops will have reduced opening hours and public transport will follow a reduced schedule.
The same will apply to most foreign, even Asian and Arab restaurants. Even if the owners don't celebrate Christmas, they likely won't bother staying open since they can't expect many customers to show up.
Finding an open restaurant for Christmas Eve and Christmas Day in Trondheim is bound to be difficult, but you may be a little bit early right now. Restaurants will likely publish their opening hours during Christmas on their web pages, but not until a bit closer to Christmas. My best guess would be to check with the larger hotels if they don't keep their restaurants open, but I just called Radisson Blu Royal Garden, one of the largest hotels in Trondheim and their restaurant is closed.
It is probably not of much help for you, but the Oslo newspaper Aftenposten traditionally writes an article shortly before Christmas about 'Where to eat during Christmas and New Year', here the article from last year. It is however in Norwegian and behind a pay wall. From the freely available introduction, we can read that only 'six restaurants are open on Christmas Eve'. They later state a disclaimer that they don't have a complete overview over all restaurants in Oslo, but I doubt that you would have found many more open places in Oslo.
In Trondheim, the city magazine trd.by published a similar overview, here the articles from 2016 and 2017. They are also in Norwegian, but at least freely available so that you can run them through an online translator. They do however not mention a single restaurant open on December 24th or 25th.