Question

Walter A. Strauss's Partial Differential Equations: An Introduction is a classic PDE textbook for the undergraduate students. While Folland's Introduction to Partial Differential Equations, is a nice one to the audience consisting of graduate students who had taken the standard first-year analysis courses but who had little background in PDE. The later one maks fairly free use of the techniques of real and complex analysis.

Could any expert here suggest a PDE book in the level between these two ones, or a complementary reading for Folland's book.

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I don't know if this is a appropriate question here --- I have no idea if the question is too localized, I learned from the internet that these two books are very classic for PDE though. Any suggestions for a good update of the question will be really appreciated.

Answer 1

Fritz John's book "Partial Differential Equations" is one of the more elementary but still substantial PDE books I have run across.

Answer 2

I like Jeffrey Rauch's book Partial Differential Equations. Fritz John's book is also very good.

Answer 3

L. Craig Evan's textbook, also called "Partial Differential Equations", is also a pretty standard text. It is aimed at the graduate level, but assumes very little analysis at the outset. Furthermore, all the analysis that you do need to know is contained in a very extensive appendix that contains such things as basic multi-variable calculus identities, metric space inequalities, measure theory, and functional analysis. I've used this book for the past two years, and I enjoy it a lot as well.

I might also be slightly biased because the author is in my department. =P

Answer 4

'Partial Differential Equations' by Paul Garabedian is an excellent text 'between' Strauss and Folland. The book rewards repeated reading, and contains a wealth of material and insight. It doesn't use the analytical machinery of modern PDE (e.g. does not use Sobolev spaces). It includes topics like the Perron construction, the properties of the Neumann function (as opposed to the Green's function) for a domain, and the Hamilton-Jacobi PDE. My advisor gave me his copy many years ago, saying 'this will be a good friend'.

Answer 5

While Evans (which I think fits your requirement) is probably the 'standard' text, I slightly prefer Renardy and Rogers' book, which covers roughly the same material.