Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I need a book covering $L^p$ theory (is it?) on PDE. Stuff should include: De Giorgi-Nash-Moser’s iteration, Harnack inequalities and Schauder estimates on elliptic/parabolic homogeneous/heterogeneous equations, together with their divergence forms.

I've found Jürgen Jost's Partial Differential Equations, whose second half provides more or less I need. Can you recommend some other books providing full details on those topics for me? Thank you~

share|cite|improve this question
Ah, 18-155 and 18-156 on OCW@MIT seem good supplements. – ziyuang Jun 13 '11 at 18:06
Haim Brezis' Functional Analysis has some facts about $L^p$ spaces, although maybe not really what you're looking for. – Beni Bogosel Jun 13 '11 at 19:08
$L^p$ theory of PDE typically cope with the properties of the solution in $L^p$ space (and Sobolev, Hölder...) of some PDEs, rather than what we learn at undergraduate courses, where solutions are smooth. – ziyuang Jun 13 '11 at 19:29
@ziyuang: The first link in your first comment does not work. – Jack Jul 19 '11 at 18:21
@Jack: Oops... 18-155 – ziyuang Jul 20 '11 at 1:51
up vote 2 down vote accepted

A reference that comes close is also

  • Michael E. Taylor: Partial Differential Equations III: Nonlinear Equations. (2nd edition)

See here: ZMATH

share|cite|improve this answer

For the elliptic case the classic reference (and the best I can think of) is "Elliptic Partial Differential Equations of Second Order" by Gilbarg and Trudinger. You'll find a very detailed exposition of Schauder's theory, Harnak inequality and maximum principles, Calderon-Zygmund and so on and so forth. For a good understanding of $L^p$ spaces in general, I agree with Beni Bogosel with the book of Brezis and also recommend Folland's "Real Analysis". It's developed in a slightly more general (and abstract) setting, because instead of $\mathbb{R}^n$ he studies arbitrary measure spaces, but the book is an excellent reference in real analysis. Hope I've been helpful...

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.