You could use

readlink /proc/$(pgrep -x -U $(id -ur) APP_NAME)/exe

or

find /proc/$(pgrep -x -U $(id -ur) APP_NAME)/exe -printf "%l\n"

to get the absolute path. PID is the process.

You could use

readlink /proc/$(pgrep -x -U $(id -ur) APP_NAME)/exe

or

find /proc/$(pgrep -x -U $(id -ur) APP_NAME)/exe -printf "%l\n"

to get the absolute path of APP_NAME running as current user.