I know quite a bit about the abstract theory of Interpolation of Banach spaces. Today I had a colleague from Environmental sciences (who used to be in our Applied Maths department) come and ask me about (complex) interpolation of Sobolev spaces. I was, in the end, able to explain enough to give him a "black box" which seemed to do enough (recover norm estimates for odd cases from formula established for even cases by partial integration techniques).
Now, the book which he'd been pointed to (by another book) was "Interpolation spaces" by Bergh and Lofstrom. I've read this, of course, but it takes a (almost caricatured) pure maths approach: you have to read it cover to cover to catch all the definition etc. So my question is:
Does anyone know of a "friendly" (applied maths style) approach to complex interpolation of Sobolev (and related function) spaces?
I'm guessing that this must exist, as it's only a small step from the classical Riesz-Thorin interpolation, which must be used by lots of people who don't particularly care about abstract Banach spaces.
Edit: Perhaps I'm being dismissive or confusing or something about "applied maths style". I don't wish to be! The book my colleague showed me said something like: "The odd case follows by interpolation. (This is not an easy argument, and we do not give it. See, for example, the book of Bergh+Lofstrom.)" I'm sort of taking this as a baseline. Many thanks for the suggestions so far-- I'll leave this open a bit longer, and then accept an answer.