Smith and Van den Bergh worked with it, and got some lovely results, in [this paper][1].  For example, they show that direct summands of polynomial rings have simple rings of differential operators in positive characteristic.   This is still open (as far as I know) in characteristic 0.  

It's a particularly interesting paper for the connections it makes with representation types.


  [1]: http://plms.oxfordjournals.org/cgi/content/short/75/1/32