Problem with texture on new mesh

Your link is brokedn anidup

It seems that the problem is with your mesh. It has a lot of doubles overlapping in the same space. I went to blender and removed doubles, but since the mesh has not thickness it deletes some of the faces too.

I recommend you re-do that part of the mesh. What I would do is the following:

1. Create a uv-sphere and reduce it's polycount from the start choosing a lower segments and rings values.

2. Go into edit mode and chop the sphere to your like.

3. Go to the modifiers and apply a Solidify modifier. This will make your mesh has a little thickness. You can edit the value to your like too. This ways the inner faces wont overlap with the outter ones. Negative thickness values will give it outwards and positive inwards.

You would have to re-map that part but I think it's the best work around.