A small percentage of iPhone 11 displays may stop responding to touch input, and the cause of this problem has been discovered to be the display module. Thankfully, Apple is providing repairs free of charge as part of the recently introduced "iPhone 11 Display Module Replacement Program for Touch Issues."
https://www.notebookcheck.net/Apple-launches-iPhone-11-repair-program-Free-repairs-for-display-issues.508141.0.html