Usage of "our" in sentences where we skip that/which are

Solution 1:

Here, "our" is a determiner, and specifically a definite determiner, while "more powerful than your computer" is a restrictive clause. In other words, "more powerful than your computer" tells you which smartphones we're checking Facebook on. If you put "our" in the sentence as well, you've already said which smartphones we're checking Facebook on, so you need to use a non-restrictive clause. You can do that by inserting "that/which are".

Consider.

I check Facebook three times on the way to work on a smartphone more powerful than your computer.

Here "a" is an indefinite determiner, so this works fine.

*I check Facebook three times on the way to work on this smartphone more powerful than your computer.

And "this" is a definite determiner, so it sounds wrong.

UPDATE: In the comments, Edwin Ashworth points out that it's not the fact that "our" is a definite determiner that makes this sentence ungrammatical. It's the fact that "our smartphones" has already completely determined what we are referring to, so we can't use a restrictive clause to narrow it any further.