The way I have always felt about this issue was that Dostoevsky did this intentionally to be a testament to Raskolnikov sanity or insanity. I agree with mgm he is caring for his sister.
If you haven't finnished the book don't read on, I will spoil it...
That is why Raskolnikov eventually ends up leaving his sister in his friend's care. (For some reason I can't remember his name

) Anyways, Raskolnikov leaves Dounia and his mother in his best friends care in my opinion because he realizes that he is about to be caught, but mainly because Raskolnikov finally realizes he is incapable of taking care of himself much less those whom he loves. So the act that seems like he had abandon every one that he loves but in reality leaving was the ultimate act of love. I feel that this ties in well with some of Dostoevsky's christian viewpoints. But that is a discusion for a later time...