I had this happen last winter. I used a mig welder to fix the offending area. First I pulled the door panel off, and removed the latch (as recommended above). Then I wire wheeled the area to remove all the paint etc. DON'T use a grinding wheel to remove the paint, the metal is very thin, a wire wheel will remove the paint but lessen the chance of significant metal removal. I welded the cracks (I had multiple cracks after close inspection). Then I made a plate to cover the entire area, marked and drilled out for the mounting bolts, door latch slot and tacked that to the door to strengthen the are and spread the load. Not a sexy repair, but functional.
I replaced the hinges, before doing this repair, but obviously didn't replace them soon enough. Figure on doing the hinges as well to prevent the same thing from happening again.
Chris