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The following question has been inspired by "Must read" papers in numerical analysis.

In 1993, Prof. Trefethen published a NA-net posting with a list of thirteen papers that he had used in the seminar Classic Papers in Numerical Analysis.

Question: In your opinion, what classic papers should be in a "must read list" of papers in the [huge] field of PDE (and related areas)?

Note: Paraphrasing Trefethen, let us intend "must read" as providing a satisfying vison of the broad scope of PDE and a sense of excitement at what a diversity of beautiful and powerful ideas have been invented in this field.

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The question is too broad and different people may have different favorites. I would recommend Brezis' book on functional analysis. It discusses the key principles of functional analysis, introduces the very versatile Sobolev spaces and then discusses existence and regularity for the basic classes of PDE's.

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One possible reference among many many others... :

H. Brezis and F. Browder, Partial differential equations in the 20th century, Advances in Mathematics 135 (1998), 76-144.

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Perelman's papers on the Poincaré conjecture have to be among the most important. I'm nowhere near capable of reading them but Terence Tao's exposition gives a sense of their depth, and is worthy in its own right:

Terence Tao: Perelman's proof of the Poincaré conjecture: a nonlinear PDE perspective (2006)

http://arxiv.org/abs/math/0610903

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