When someone is determined to think the worst of you, how do you handle it?

Do you try to prove them wrong, to get them to see that they were wrong about you? After a while, do you just decide it’s a waste of your time? After all, if someone believes the worst about you, especially when their opinion is not based on facts, what is the point? Some people are determined to believe what they want to believe, and there is no changing their mind, so, why not live up to their expectations?