Hi gothtini,
well explained. It would be good to see the mesh together with the shader to recommend a solution.
So far of course you can try to bevel the upper edge with the command "bevel" under =>modelling=>edit mesh.
If you have a mesh on top of your object with a center area you can try also to mark the center face or vertice and move it up under usage of "soft selection" under tool settings. Here you can adjust the curve and radius and this also should be able to give you the desired effect.
One other option would be also to lower down the upper outside edge line and simply hit "3"" to smooth the object out. But this depends a little bit on the mesh, which is not visible right now.

Best regards

Jens