Lawrence C. Evans

I've seen a lot of positive reviews of this text, and I feel the need to explain some cons of this book. Before that, I will say this is probably the best introduction to PDE theory out there. This is NOT a book for people looking for a dissertation on undergraduate methods of solution (separation of variables, fourier series, etc.). If that is what you are looking for, go to Haberman or perhaps Strauss.

Ok, so here are the problems I see with this text. First, there is no mention of distributions in this book. Evans addresses this in the intro., saying it's not necessary. I find that hard to swallow, given that fundamental solutions play a big part in the text. Despite this, Evans devotes parts of the book to going into very esoteric subjects like mean value theorems for the heat equation. The other glaring gap in this text is the absence of Schauder estimates; a corner-stone for linear elliptic theory. On a note of personal preference, I would have like to have seen more of the book dedicated to a functional analytic foundation; the appendicies that are present are simply not enough.

Overall, the book gives a decent introduction; but is far from being self-contained and is not enough of a foundation for people wishing to pursue research in PDE. Evans does acknowledge this in his introduction, but I think its something that is frequently overlooked in reviews of this text.… (mais)