I'm currently working on my PhD thesis. I have several suggested problems to work on, some of them are very similar to some problems that my advisor have worked before and published already, either in his thesis or papers. Basically, the main difference is in the dimension of some singular sets (his works are mainly on the isolated case, but I'm working on a case with a far more hairier, non-isolated singular set), which we were unsure if the argument would hold but it seems that the adaptations I've made were fine.
Not that the nature of the problem matters, but the approach I'm making worries me. It seem to me that if there would be a 'railroad' to prove the results I'm working on, it would be the same path that he followed to write his own results, with different objects. That's the way I've been advised to work, and it's been producing results.
Is this a reproachable approach? Of course, there is the problem of using similar introductions (and in that subject I've read this previous question Does this qualify as "self plagiarism" or something? , only one that got close to my problem) sinde the objects being studied by me and that has been studied by him were so similar.