The effect due to the curved image is exactly one of the main reasons for corner softness with rectilinear wideangles as Paul has explained. Corners are more close in terms of the lens's focus distance and have to be covered by DOF.
The effect is increased by:
1) close subject distance
2) open aperture
3) small dome radius
Comparisons have shown that a well chosen dioptre can help to increase corner performance as the focus range is extended to a greater range towards infinity.
Fisheyes are better in this respect. Fisheyes do focus on a curved image. Perfect lens to shoot a dome’s curved virtual image.
Julian