After publishing an introduction to the Navier-Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.
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From the reviews:
"This book is based on a set of lecture notes prepared by the author from a graduate course ... . The main themes are Sobolev spaces and interpolation theory. ... The book contains 42 chapters, each intended to contain the amount of material which would be suitable for a graduate lecture. ... As well as being an excellent source of material for a graduate course on topics ... this book contains a great deal which will be of interest to the seasoned researcher." (W. D. Evans, Zentralblatt MATH, Vol. 1126 (3), 2008)
"This is a book that has grown out of a graduate course taught by the author in 2000. It keeps the structure of a set of lectures ... . Many interesting remarks are given along the text, and by means of a large number of footnotes the author explains many anecdotes and personal experiences related with people associated to the development of the topics included in the text. This book can be useful not only as a source in graduate courses, but also for researchers." (Joan L. Cerdà, Mathematical Reviews, Issue 2008 g)
"This book is based on a set of lecture notes prepared by the author from a graduate course ... . The main themes are Sobolev spaces and interpolation theory. ... The book contains 42 chapters, each intended to contain the amount of material which would be suitable for a graduate lecture. ... As well as being an excellent source of material for a graduate course on topics ... this book contains a great deal which will be of interest to the seasoned researcher." (W. D. Evans, Zentralblatt MATH, Vol. 1126 (3), 2008)
"This is a book that has grown out of a graduate course taught by the author in 2000. It keeps the structure of a set of lectures ... . Many interesting remarks are given along the text, and by means of a large number of footnotes the author explains many anecdotes and personal experiences related with people associated to the development of the topics included in the text. This book can be useful not only as a source in graduate courses, but also for researchers." (Joan L. Cerdà, Mathematical Reviews, Issue 2008 g)