If you want to make a difference, first address POVERTY. The best teachers in the world don't overcome all the negative, long-term effects on learning poverty creates.
Equitable funding helps, too. Clean, safe, modern schools in those "difficult" areas might also make a difference.
As would before and after programs to tutor, to help with homework, etc..
Offering to pay veteran teachers more to teach in "difficult" areas is a cheap way to avoid investing in what those schools, and those communities, really need.
Edited to add:
I teach in a "difficult" area. Not an inner-city, but a rural area rife with poverty. It's a different set of problems, but the effect is the same.
Many students whose home lives are chaotic and dysfunctional. Many who are homeless, many in foster care, many who live with family other than their parents. A meth culture. An anti-intellectual culture. High rates of adult illiteracy, low rates of adult education and income.
We have some great teachers. We spend more time worrying about making sure Johnny got to eat today, Susie is going to get the glasses she needs, everything is okay at Ben's house, because they don't have a phone and we haven't been able to reach them, whether it's safe to let Fred's parents know about his misbehavior, whether Jane has a ride to school from where ever she stayed last night, whether Annie's family is going to yank her out of school again, like they've done every year, and "homeschool" her out in the back of beyond, because they don't trust "the system," whether any of them ever read any of the newsletters, notices, or announcements we send home, whether Jorge's family will be going back to Mexico again, whether we can overcome Sam's resistance to school in general; he wants to drop out at the end of this year when he's done with 8th grade, and his family will probably let him. Whether we can get past the social/emotional/behavioral dysfunctions of so many kids who have grown up abused or neglected or just in need...
We spend way more time worrying about all of that than whether or not Billy, our class, or our school is going to make AYP. We see that Carol is 3 years behind in skill levels, and we breathe a sigh of relief that she is at school every day, that she has made some friends, and that she is able to function without going into a violent rage or a catatonic state; she wasn't last year. We're glad when she learns, of course.
We're also intimately aware of Maslow's hierarchy, and that the state content standards are higher on that pyramid than some of our kids can reach without interventions in their lives outside of school.
If you really want to address learning in "difficult" areas, address the lower levels of the pyramid.