An Introduction to Partial Differential Equations.

From the reviews of the second edition:

"This second edition of the book from 1993 is still one of the most modern books about PDEs. ... There is a number of ... new examples and exercises, or new sections about Sobolev spaces and nonlinear variational problems. The book is written very well and can be strongly recommended as a textbook for a number of PDE courses. The presentation of a number of subjects is the best available in the literature." (G. Schneider, Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 84(10-11), 2004)

"An Introduction to Partial Differential Equations (2nd ed.) is a very careful exposition of functional analytic methods applied to PDEs. ... a self-contained text that can be used as the basis of an advanced course in PDEs or as an excellent guide for self-study by a motivated reader. ... acts and feels like a standard book in a specific area of mathematics. ... The Renardy and Rogers text contains a large number of problems ... . For students, these problems will be challenging and interesting. ... is a great book." (Ronald B. Guenther, Enrique A. Thomann, SIAM Reviews, Vol. 47(1), 2005)

"The purpose of this book is to put the topic of differential equations on the same footing in the graduate curriculum as algebra and analysis. ... the authors describe it as a book for three or four semesters. ... they succeed admirably. The book is extremely well-written with lots of examples and motivation for the theory." (Gary M. Lieberman, Zentralblatt MATH, Vol. 1072, 2005)