Concerned About vs. Concerned With

to be concerned with = “to deal with, to be focused on” or “to be occupied”

this essay is concerned with the problem of overpopulation

concerned with writing my doctoral thesis

to be concerned about = “to be worried about”

this essay is concerned about the problem of overpopulation

the author of this essay is concerned about the problem of overpopulation

Note that in other forms, when there is no preposition to distinguish these meanings, the meaning of concern varies and in some cases can be ambiguous. Depending on context, “This letter concerns me,” for example, could mean that the letter is about me, or it could mean that the letter causes me to feel concern or worry.