I ask this question in MO. then a user suggested me to ask it at MSE. But I could not find Elliptic PDE tag or index theory tag. Is it a good idea to suggest to MSE to produce such tags?
Elliptic equations already exists.
I am slightly skeptical about "index theory": this phrase appears in 5 questions, and they are on different topics. While I do not strongly object to the tag, my expectation is that in a year's time we would find it filled mostly with questions about changing the index from $k$ to $k+1$ in some sum.