I’m running the latest openhabian installation and for a while now I get crashes without knowing where they come from. They end up in a “java.lang.OutOfMemoryError: Java heap space” error.
openhabian seems to use the openJDK - could it be a solution to switch over to Oracle Java - and if yes, how would I achieve this?
openHABian uses Zulu. Its basically an optimized openJDK.
For ARM (rPis), Zulu embedded is used.
You can try to switch to Oracle but I am afraid that your problems will not go away (I don’t know what is the root cause of your problems 
)
There are many guides online on how to deploy Oracle JVM on Raspberry Pi. Remember to use update-alternatives --config java after you install another JVM to select it as default.