For a long time, I was making closeup photographs of flat surfaces using my cropped DLSR and Canon EF 50/1.4 lens. The scene was illuminated by an external flash. The focusing distance was the closest as the lens could give (0.45m). The sharpness of the image at the center and the corners was suitable to me.
Recently I have switched to a full frame camera and noticed that all the photographs are very soft at the corners (however sharp at the center). For the first time I understood that this lens (50/1.4) may be not the best lens for the kind of the photos I'm taking. Some people say that macro lens is more suitable for my situation.
Here's the 100% crops from the photo I've made using Canon EF 50/1.4 on a full frame sensor at the closest focusing distance (approx. 0.45m), f/11, ISO 100, manual focusing using liveview, camera standing on a tripod, direct external speedlight type flash to the right of subject:
So, here's the question: what lenses could solve the problem of soft sharpness at the corners in my situation?
Here is an example from dxomark: you can look at details for specific lens and camera, and how it performs at different apetures.
Your observation is correct. However, all lens shows this effect, but to a different degree.
I suggest checking out e.g. this lens comparison tool. You will see the actual behavior of different lenses.
For better understanding, you should learn to read and use MTF charts. A very good explanation (with examples for the Canon 50 mm f/1.4 !) can be found through this link.
In general, you want the lines for your aperture to be as higher up and as flat as possible.
For the reason TFuto noted, that the in-focus region is actually a sphere "touching" the center point of your plane, it is best to use a lens with a rather large focal distance, and shoot from farther away. This will increase the radius of that sphere, which means the difference between center and corner won't be as big. Of course, it should still be a lens with good corner sharpness characteristics...