I am looking for a basic set of notes/text that deals with the basics of PDEs with measure valued right hand sides. Even an answer here that answers the following questions would be good:
1) A precise formulation of the problem. I assume it's something like wanting to solve $$-\Delta u = \delta$$ where $\delta$ is the Dirac delta function.
2) Function spaces used in this field, and what elementary theorems/techniques are used to obtain well-posedness? (For example, in the ordinary elliptic case I would say: Sobolev spaces with Lax-Milgram etc etc).
Thank you
I think you might like this monograph. Also, take a look in his site. Ponce studied with Brezis, so it is worth to take a look in his work and also on Brezis work. Brezis has some papers about solving partial differential equations involving measures: take a look here.