Book searching in Elliptic Equation

Question

I am learning a course with the subject of Elliptic Equations. If you know about it, please recommend me a book on Elliptic Equations.

And if that's possible, someone post these books/author/...that I should read and do exercises/homework.

Thanks!

Answer 1

Because I don't know what kind of course is it, I will refer to you four books.

The first one is a good and standard reference and gives you a general view on Partial Differential equations. It is the book of Evans.

The second one is more focused on Elliptic Partial Differential Equations, but it contains almost all (if not all) the basic information you need to know in this area (Elliptic Partial Differential Equation). It is the book of Gilbard-Trudinger.

The third book is more specialized, but can be seen as a complement of Gilbard-Trudinger book. It is the book of Han-Lin.

The fourth is Brezis book. Although it is not a book concerned only with PDE, it gives you the necessary tools to understand most part of the modern treatment of PDE.

Answer 2

To Tomas' excellent list above I would add Ladyzhenskaya and Uraltseva's Linear and Quasilinear Elliptic Equations.

In general, I would remark that Evans is a great introduction to PDE in general. Brezis' book is mostly about Sobolev spaces with some applications to PDE theory. Han-Lin a great set of introductory lectures to elliptic PDE once you know Sobolev spaces. I would not advise trying to read Gilbarg-Trudinger on first approach to any topic, because it is quite complete and exhaustive, handling very general cases, but it has some excellent problems at the back of every chapter. Ladyzhenskaya and Uraltseva's book can offer an alternative "style" of explanation, which I often find quite intuitive and less abstract than, say, G-T.