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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~

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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
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@Jack: Oops... 18-155 –  ziyuang Jul 20 '11 at 1:51
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1 Answer 1

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

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