Lawrence C Evans Partial Differential Equations Second Edition 2010 Pdf
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I would also like to add Peter Olver's "Introduction to partial differential equations" to this growing list. It was published in 2014 and is very suitable for self-studying. The preface does a good job of explaining the various topics and prerequisites required to understand PDEs which I hadn't appreciated until I read it in the book-highly recommended. Solutions to about 20% of exercises are available on the author's website.
I have not read much of this book, but I found this tidbit interesting- Chapter 5 ("Equations in n-dimensions") is a good introduction to PDEs in two dimensions. Author writes "The idea is to present the theory of PDEs and then to conduct a detailed and systematic study of three particular types of PDE problems: (1) boundary value problems; (2) initial value problems; and (3) partial differential equations with nonlocal terms. A much longer and more standard treatment of these subjects can be found, for example, in Coddington and Levinson's te{CL} textbook."
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