How to remove vignetting and color cast from wide angle lens?

After shooting several images with the Samyang 12mm f/2 for mirrorless APS-C, I noticed it produces a quite strong color cast. It looks like green vignetting. As far as I know, this isn't uncommon for wide-angle lenses.

I experimented with radial filters in Lightroom, but the results weren't satisfying. Is there a method or tool to consistently remove this cast?

Here is an example taken at daylight, ISO 200 and f 5.6, which isn't even wide open. I cranked up saturation to make the defect more apparent.

Here is the same image without editing:

Answer

After a lot of searching I found some tools that do exactly what I needed:

Both Cornerfix and the DNG Flat Field PlugIn work direktly (and only) on DNG files, are easy to use and produce good results; batch processing is possible.

All these tools work the same way (as JerryTheC suggested): You take a "Flat Field Image", which is an evenly illuminated and uniformly white image. Some suggest shooting a white wall; I found it much easier to cover the lens with a white piece of plastic (a kitchen cutting board, in my case). It helps to set the focus to infinity so that the white filter is out of focus.

The tools then use the information of this image to cancel out any brightness falloff or color cast to the image corners, even dust bunnies on the sensor or lense can sometimes be removed with this.