iPhone 11 keeps turning off itself

if it was me then I would check the batt health

Understand your iPhone battery usage and health - Apple Support

if it was under 80% then I would consider having the batt replaced

iPhone Battery Replacement - Apple Support

maybe also read

About the battery and performance of iPhone 11 and later - Apple Support

and maybe iPhone Battery and Performance - Apple Support

and Batteries - Maximizing Performance - Apple

1. Follow the Apple article to resolve the issue --> If your iPhone, iPad, or iPod touch won't turn on or is frozen ...
2. If not resolved; please follow the steps in the following link for support with this issue: If your iOS device restarts or displays the Apple logo or a spinning gear unexpectedly
3. You still see a black screen after charging, force restarting, following the steps in this article.
   1. You see a black screen, but you can hear alerts, sounds, and vibrations.
   2. The screen remains black, but the device chirps when you unmute it and connect it to power.
   3. Your screen is on, but it doesn't respond when you tap, slide, or try other gestures. 
   4. You can't force your device to restart because a button is broken or stuck.
   5. Your device is stuck on the Apple logo, displays a solid color, or isn't recognized in iTunes.
   6. Contact Apple Support to set up service if you have any of the above issues:
4. Please follow the steps in the following Apple Video for support with this issue: