What can I do if I don’t completely understand a paper? Our team finished a paper 3 months ago. However, we use a result from another paper in a very top journal (one of the best). There are quite a lot misprints and somewhat mistakes. We can fix most of them but one inequality which they didn't have explanation why this inequality is true. We have spent 3 months to ask people (some extremely top mathematicians, they published many papers in the top 5 journals) and no one understand...We also asked the authors, but it seems that they don't want to explain that to us...We are really lost and don't know what to do...Shall we submit our paper? We really can not make sure that the inequality is true...

PS. This result is crucial in our proof...

Now, we have clarified the 'gap', there are some problems in the proof, the assertions are not accurate/correct. However, luckily, the final result is correct. After discussing with one of the authors, we confirmed that it is a gap and it took us quite some time to fix it.  

Well, some people told me that the 'big guys' do not care about the details. I am not sure whether these incorrect details would lead to wrong theorem. As a young scholar,   I have to say that I am a little bit disappointed at math research (well, maybe my field).
Ask on mathoverflow!

It's a site like this, but for math at research level. There is incredible expertise in all fields of math (I know of) over there. Before you ask, look at "How to ask"  and also take a look around at the site to get a feel for how the folks roll.