I saw this question, but I think the answer didn't fully address what I want to know about it:

Nash's paper on parabolic equations.

It says almost everything developed later in elliptic and parabolic equations depends on Di-Giorgi and Nash's work, but I haven't seen Nash's approach exposed nearly as frequently as De-Giorgi's in various books/lecture notes. So, my question is: Do you have a good reference for Nash's approach to his famous theorem and later developments based on that? NOTE: I'm not asking for Nash's own paper, which I already have. What I'm more interested in is an exposition with references to more recent developments.


2 Answers 2


There is an extremely useful and clear presentation by Fabes and Stroock http://link.springer.com/article/10.1007%2FBF00251802


If you understand spoken French, this talk by Villani might be of interest: https://youtu.be/F7wSqLetdGM

  • $\begingroup$ Je comprends le francais: ca me semble d'etre une vulgarisation qui manque des details desires par @FanZheng $\endgroup$
    – Yemon Choi
    Mar 6, 2016 at 21:49
  • $\begingroup$ Should I delete my answer and just add the link in a comment then? $\endgroup$ Mar 6, 2016 at 21:57
  • $\begingroup$ Well, I'm just not sure it's useful! Unless you can point us to a particular segment of the talk which actually addresses what the OP was asking for... $\endgroup$
    – Yemon Choi
    Mar 6, 2016 at 22:29
  • $\begingroup$ At around 1:16:00, Villani explains, answering a question, that the fact that knowing the solution is continuous is useful to solve the PDE numerically. I don't know whether this fits what the OP looks for, but anyway, if it ever turns out that he or she doesn't understand spoken French, my answer will have been useless in any case! $\endgroup$ Mar 6, 2016 at 22:46

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